## Archive for the ‘diseases’ Category

### Herd immunity

February 14, 2019

I have a long term interest in examples where mathematics has contributed to medicine. Last week I heard a talk at a meeting of the Mainzer Medizinische Gesellschaft about vaccination. The speaker was Markus Knuf, director of the pediatric section of the Helios Clinic in Wiesbaden. In the course of his talk he mentioned the concept of ‘herd immunity’ several times. I was familiar with this concept and I have even mentioned it briefly in some of my lectures and seminars. It never occurred to me that in fact this is an excellent example of a case where medical understanding has benefited from mathematical considerations. Suppose we have a population of individuals who are susceptible to a particular disease. Suppose further that there is an endemic state, i.e. that the disease persists in the population at a constant non-zero level. It is immediately plausible that if we vaccinate a certain proportion $\alpha$ of the population against the disease then the proportion of the population suffering from the disease will be lower than it would have been without vaccination. What is less obvious is that if $\alpha$ exceeds a certain threshold $\alpha_*$ then the constant level will be zero. This is the phenomenon of herd immunity. The value of $\alpha_*$ depends on how infectious the disease is. A well-known example with a relatively high value is measles, where $\alpha$ is about $0.95$. In other words, if you want to get rid of measles from a population then it is necessary to vaccinate at least 95% of the population. It occurs to me that this idea is very schematic since measles does not occur as a constant rate. Instead it occurs in large waves. This idea is nevertheless one which is useful when making public health decisions. Perhaps a better way of looking at it is to think of the endemic state as a steady state of a dynamical model. The important thing is that this state is asymptotically stable in the dynamic set-up so that it recovers from any perturbation (infected individuals coming in from somewhere else). It just so happens that in the usual mathematical models for this type of phenomenon whenever a positive steady state (i.e. one where all populations are positive) exists it is asymptotically stable. Thus the distinction between the steady state and dynamical pictures is not so important. After I started writing this post I came across another post on the same subject by Mark Chu-Carroll. I am not sad that he beat me to it. The two posts give different approaches to the same subject and I think it is good if this topic gets as much publicity as possible.

Coming back to the talk I mentioned, a valuable aspect of it was that the speaker could report on things from his everyday experience in the clinic. This makes things much more immediate than if someone is talking about the subject on an abstract level. Let me give an example. He showed a video of a small boy with an extremely persistent cough. (He had permission from the child’s parents to use this video for the talk.) The birth was a bit premature but the boy left the hospital two weeks later in good health. A few weeks after that he returned with the cough. It turned out that he had whooping cough which he had caught from an adult (non-vaccinated) relative. The man had had a bad cough but the cause was not realised and it was attributed to side effects of a drug he was taking for a heart problem. The doctors did everything to save the boy’s life but the infection soon proved fatal. It is important to realize that this is not an absolutely exceptional case but a scenario which happens regularly. It brings home what getting vaccinated (or failing to do so) really means. Of course an example like this has no statistical significance but it can nevertheless help to make people think.

Let me say some more about the mathematics of this situation. A common type of model is the SIR model. The dependent variables are $S$, the number of individuals who are susceptible to infection by the disease, $I$, the number of individuals who are infected (or infectious, this model ignores the incubation time) and $R$, the number of individuals who have recovered from the disease and are therefore immune. These three quantities depend on time and satisfy a system of ODE containing a number of parameters. There is a certain combination of these parameters, usually called the basic reproductive rate (or ratio) and denoted by $R_0$ whose value determines the outcome of the dynamics. If $R_0\le 1$ the infection dies out – the solution converges to a steady state on the boundary of the state space where $I=0$. If, on the other hand, $R_0>1$ there exists a positive steady state, an endemic equilibrium. The stability this of this steady state can be examined by linearizing about it. In fact it is always stable. Interestingly, more is true. When the endemic steady state exists it is globally asymptotically stable. In other words all solutions with positive initial data converge to that steady state at late time. For a proof of this see a paper by Korobeinikov and Wake (Appl. Math. Lett. 15, 955). They use a Lyapunov function to do so. At this point it is appropriate to mention that my understanding of these things has been improved by the hard work of Irena Vogel, who recently wrote her MSc thesis on the subject of Lyapunov functions in population models under my supervision.

### New hope for primary progressive multiple sclerosis?

April 12, 2017

Multiple sclerosis is generally classified into three forms. The relapsing-remitting form is the most common initial form. It is characterized by periods when the symptoms get much worse separated by periods where they get better. The second form is the primary progressive form where the symptoms slowly and steadily get worse. It is generally thought to have a worse prognosis than the relapsing-remitting form. In many cases the relapsing-remitting form converts to a progressive form at some time. This is then the secondary progressive form. In the meantime there is a big variety of drugs on the market which are approved for the treatment of the RR form of MS. They cannot stop the disease but they can slow its progression. Until very recently there was no drug approved for the treatment of progressive MS. This has now changed with the approval of ocrelizumab, an antibody against the molecule CD20 which is found on the surface of B cells. It has been approved for both the RR form and some cases of the progressive form of MS.

Ocrelizumab acts by causing B cells to be killed. It has been seen to have strong positive effects in combatting MS in some cases. This emphasizes the fact that T cells, usually regarded as the main culprit causing damage during MS, are not alone. B cells also seem to play an important role although what role that is is not so clear. There previously existed an antibody against CD20, rituximab, which was used in the therapy of diseases other than MS. Ocrelizumab has had problemtic side effects, with a high frequency of infections and a slightly increased cancer risk. For this reason it has been abandoned as a therapy for rheumatoid arthritis. On the other hand the trial for MS has less problems with side effects.

One reason not to be too euphoric about this first treatment for progressive MS is the following. It has been shown to be effective against patients in the first few years of illness and those where there are clear signs of inflammatory activity in MRT scans. This suggests to me a certain suspicion. The different types of MS are not clearly demarcated. Strong activity in the MRT is typical of the RR form. So I wonder if the patients where this drug is effective are perhaps individuals with an atypical RR form where the disease activity just does not cross the threshold to becoming manifest on the symptomatic level for a certain time. This says nothing against the usefuleness of the drug in this class of patients but it might be a sign that its applicability will not extend to a wider class of patients with the progressive form in the future. It also suggests caution in hoping that the role of B cells in this therapy might help to understand the mechanism of progressive MS.

### Herbal medicine and its dangers

December 18, 2016

I recently heard a talk by Thomas Efferth of the Institute for Pharmacology of the University of Mainz on herbal medicine. There is a common point of view that substances derived from plants are harmless and good while the chemical drugs of standard medicine are evil. The speaker emphasized that plants have good reasons for not being good to those who eat them. They do not have immune systems of the type we do and they cannot run away and so it is natural that they use poisons to defend themselves. Herbal medicines are effective in some cases but they need to be subject to controls as much as do substances obtained by artificial chemical means. In the talk a number of examples of the dangers of ‘natural’ medicines were presented and I will write about some of them here.

The first example is that of Aristolochia. This a large genus of plants, some of which are poisonous. One of these, Aristolochia clematitis, has been extensively used in herbal medicine. It was used extensively in the west in ancient times and is used in traditional Chinese medicine until today. In the talk the story was told of an incident which happened in Belgium. There was a product sold as a means of losing weight which contained a Chinese plant. It sold so well that the manufacturer’s supplies of the plant were running out. When more was ordered a fateful mistake took place. There are two plants which have the same name in China. The one is that which was originally contained in the weight-loss product. The other is the poisonous Aristolochia fangchi and it was the one which was delivered. This led to more than 100 cases of kidney failure in the people using the product. Another way in which plants can be dangerous is as weeds in crop fields. In the Balkans contamination of grain with Aristolochia clematitis led to a kidney disease called Balkan nephropathy, with 35000 recorded cases. The substance, aristolochic acid, which is responsible for the kidney toxicity is also known to be a strong carcinogen. Interestingly, this substance is not poisonous for everyone and its bad effects depend a lot on the variability in liver enzymes among individuals.

A class of substances used by many plants to protect themselves against insects are the pyrrolizidine alkaloids. These substances are hepatotoxic and carcinogenic. They may move through the food chain being found, for instance, in honey. It has been noted that there may be risks associated to the amount of these substances contained in medicinal herbs used both in the West and in China. It was mentioned in the talk that drinking too much of certain types of herbal tea may be damaging to health. The problem is usually not the plants that are the main components of the teas but other plants which may be harvested with them in small quantities. There is at least one exception to this, namely coltsfoot (Tussilago farfara). In one case the death of an infant due to liver disease is believed to be due to the mother drinking this type of tea during pregnancy. After that the sale of coltsfoot was banned in Germany.

There were some remarks in the talk on heavy metals which I found quite suprising. One concerned ayurvedic medicine which has an aura of being gentle and harmless. In fact in many of these substances certain heavy metals are added delibrately (lead, mercury and arsenic). According to Wikipedia more than 80 cases of lead poisoning due to ayurvedic ‘medicines’ have been recorded. Another remark was that there can be significant concentrations of heavy metals in tobacco smoke. The negative health effects of smoking are sufficiently well known but this aspect was new to me.

Another theme in the talk was interactions between herbal medicines and normal drugs. Apparently it is often the case that patients who use herbal remedies are afraid to mention this to their doctors since they think this may spoil the relationship to their practitioner. Then it can happen that a doctor is suprised by the fact that a drug he prescribes is not working as expected. Little does he know that the patient is secretly taking a ‘natural’ drug in parallel. An example is St. John’s wort which is sometimes taken as a remedy for depression. It may work and it has no direct negative effects but it can be problematic because it reduces the effects of other drugs taken at the same time, e.g. the contraceptive pill. It changes the activity of liver enzymes and causes them to eliminate other drugs from the body faster than would normally happen, thus causing an effective reduction of the dose.

We are surrounded by poisonous plants. I was always sceptical of the positive effects of ‘natural’, plant-derived medicines. Now I have realised how seriously the dangers of these substances should be taken.

### Modern cancer therapies

October 28, 2016

I find the subject of cancer therapies fascinating. My particular interest is in the possibility of obtaining new insights by modelling and what role mathematics can play in this endeavour. I have heard many talks related to these subjects, both live and online. I was stimulated to write this post by a video of Martin McMahon, then at UCSF. It made me want to systematize some of the knowledge I have obtained from that video (which is already a few years old) and from other sources. First I should fix my terminology. I use the term ‘modern cancer therapies’ to distinguish a certain group of treatments from what I will call ‘classical cancer therapies’. The latter are still of central importance today and the characteristic feature of those I am calling ‘modern’ here is that they have only been developed in the last few years. I start by reviewing the ‘classical therapies’, surgery, radiotherapy and chemotherapy. Surgery can be very successful when it works. The aim is to remove all the cancerous cells. There is a tension between removing too little (so that a few malignant cells could remain and restart the tumour) and too much (which could mean too much damage to healthy tissues). A particularly difficult case is that of the glioma where it is impossible to determine the extent of the tumour by imaging techniques alone. An alternative to this is provided by the work of Kristin Swanson, which I mentioned in a previous post. She has developed techniques of using a mathematical model of the tumour (with reaction-diffusion equations) to predict the extent of the tumour. The results of a simulation, specific to a particular patient, is given to the surgeon to guide his work. In the case of radiotherapy radiation is used to kill cancer cells while trying to avoid killing too many healthy cells. A problematic aspect is that the cells are killed by damaging their DNA and this kind of damage may lead to the development of new cancers. In chemotherapy a chemical substance (poison) is used with the same basic aim as in radiotherapy. The substance is chosen to have the greatest effect on cells which divide frequently. This is the case with cancer cells but unfortunately they are not the only ones. A problem with radiotherapy and chemotherapy is their poor specificity.

Now I come to the ‘modern’ therapies. One class of substances used is that of kinase inhibitors. The underlying idea is as follows. Whether cells divide or not is controlled by a signal transduction network, a complicated set of chemical reactions in the cell. In the course of time mutations can accumulate in a cell and when enough relevant mutations are present the transduction network is disrupted. The cell is instructed to divide under circumstances under which it would normally not do so. The cells dividing in an uncontrolled way constitute cancer. The signals in this type of network are often passed on by phosphorylation, the attachment of phosphate groups to certain proteins. The enzymes which catalyse the process of phosphorylation are called kinases. A typical problem then is that due to a mutation a kinase is active all the time and not just when it should be. A switch which activates the signalling network is stuck in the ‘on’ position. This can in principal be changed by blocking the kinase so that it can no longer send its signals. An early and successful example of this is the kinase inhibitor imatinib which was developed as therapy for chronic myelogenous leukemia (CML). It seems that this drug can even cure CML in many cases, in the sense that after a time (two years) no mutated cells can be detected and the disease does not come back if the treatment is stopped. McMahon talks about this while being understandibly cautious about using the word cure in the context of any type of cancer. One general point about the ‘modern’ therapies is that they do not work for a wide range of cancers or even for the majority of patients with a given type of cancer. It is rather the case that cancer can be divided into more and more subtypes by analysing it with molecular methods and the therapy only works in a very specific class of patients, having a specific mutation. I have said something about another treatment using a kinase, Vemurafenib in a previous post. An unfortunate aspect of the therapies using kinase inhibitors is that while they provide spectacular short-term successes their effects often do not last more than a few months due to the development of resistance. A second mutation can rewire the network and overcome the blockade. (Might mathematical models be used to understand better which types of rewiring are relevant?) The picture of this I had, which now appears to me to be wrong, was that after a while on the drug a new mutation appears which gives the resistance. The picture I got from McMahon’s video was a different one. It seems that the mutations which might lead to resistance are often there before treatment begins. They were in Darwinian competition with other cells without the second mutation which were fitter. The treatment causes the fitness of the cells without the second mutation to decrease sharply. This removes the competition and allows the population of resistant cells to increase.

Another drug mentioned by McMahon is herceptin. This is used to treat breast cancer patients with a mutation in a particular receptor. The drug is an antibody and binds to the receptor. As far as I can see it is not known why the binding of the antibody has a therapeutic effect but there is one idea on this which I find attractive. This is that the antibodies attract immune cells which kill the cell carrying the mutation. This gives me a perfect transition to a discussion of a class of therapies which started to become successful and popular very recently and go under the name of cancer immunotherapy, since they are based on the idea of persuading immune cells to attack cancer cells. I have already discussed one way of doing this, using antibodies to increase the activities of T cells, in a previous post. Rather than saying more about that I want to go on to the topic of genetically modified T cells, which was also mentioned briefly here.

I do not know enough to be able to give a broad review of cellular immunotherapy for cancer treatment and so I will concentrate on making some comments based on a video on this subject by Stephan Grupp. He is talking about the therapy of acute lymphocytic leukemia (ALL). In particular he is concerned with B cell leukemia. The idea is to make artificial T cells which recognise the surface molecule CD19 characteristic of B cells. T cells are taken from the patient and modified to express a chimeric T cell receptor (CAR). The CAR is made of an external part coming from an antibody fused to an internal part including a CD3 $\zeta$-chain and a costimulatory molecule such as CD28. (Grupp prefers a different costimulatory molecule.) The cells are activated and caused to proliferate in vitro and then injected back into the patient. In many cases they are successful in killing the B cells of the patient and producing a lasting remission. It should be noted that most of the patients are small children and that most cases can be treated very effectively with classical chemotherapy. The children being treated with immunotherapy are the ‘worst cases’. The first patient treated by Grupp with this method was a seven year old girl and the treatment was finally very successful. Nevertheless it did at first almost kill her and this is not the only case. The problem was a cytokine release syndrome with extremely high levels of IL-6. Fortunately this was discovered just in time and she was treated with an antibody to IL-6 which not only existed but was approved for the treatment of children (with other diseases). It very quickly solved the problem. One issue which remains to be mentioned is that when the treatment is successful the T cells are so effective that the patient is left without B cells. Hence as long as the treatment continues immunoglobulin replacement therapy is necessary. Thus the issue arises whether this can be a final treatment or whether it should be seen a preparation for a bone marrow transplant. As a side issue from this story I wonder if modelling could bring some more insight for the IL-6 problem. Grupp uses some network language in talking about it, saying that the problem is a ‘simple feedback loop’. After I had written this I discovered a preprint on BioRxiv doing mathematical modelling of CAR T cell therapy of B-ALL and promising to do more in the future. It is an ODE model where there is no explicit inclusion of IL-6 but rather a generic inflammation variable.

### Hepatitis C

May 29, 2016

I once previously wrote something about hepatitis C in this blog which was directed to the mathematical modelling aspects. Here I want to write about the disease itself. This has been stimulated by talks I heard at a meeting of the Mainzer Medizinische Gesellschaft. The speakers were Ralf Bartenschlager from Heidelberg and and Stefan Zeuzem from Frankfurt. The first speaker is a molecular biologist who has made important contributions to the understanding of the structure and life cycle of the virus. For this work he got the 2015 Robert Koch prize together with Charles Rice from the Rockefeller University. The second speaker is a clinician.

Hepatitis C is transmitted by blood to blood contact. According to Zeuzem the main cause of the spread of this disease in developed countries is intravenous drug use. Before there was a test for the disease it was also spread via blood transfusions. (At one time the risk of infection with hepatitis due to a blood transfusion was 30%. This was mainly hepatitis B and by the time of discovery of hepatitis C, when the risk from hepatitis B had essentially been eliminated, it had dropped to 5%.) He also mentioned that there is a very high rate of infection in certain parts of Egypt due to the use of unsterilized needles in the treatment of other diseases. Someone asked how the disease could have survived before there were injections. He did not give a definitive answer but he did mention that while heterosexual contacts generally carry little risk of infection with this virus homosexual contacts between men do carry a significant risk. The disease typically becomes chronic and has few if any symptoms for many years. It does have dramatic long-term effects, namely cirrhosis and cancer of the liver. He showed statistics illustrating how public health policies have influenced the spread of the disease in different countries. The development in France has been much more favourable (with less cases) than in Germany, apparently due to a publicity campaign as a result of political motives with no direct relevance to the disease. The development in the UK has been much less favourable than it has even in Germany due an almost complete lack of publicity on the theme for a long time. The estimated number of people infected in Germany is 500000. The global number is estimated as 170 million.

There has been a dramatic improvement in the treatment of hepatitis C in the past couple of years and this was the central theme of the talks. A few years ago the situation was as follows. Drugs (a combination of ribavirin and interferon $\alpha$) could be used to eliminate the virus in a significant percentage of patients, particularly for some of the sub-types of the virus. The treatment lasted about a year and was accompanied by side effects that were so severe that there was a serious risk of patients breaking it off. Now the treatment only lasts a few weeks, it cures at least 95% of the patients and in many situations 99% of them. The side effects of the new treatments are moderate. There is just one problem remaining: the drugs for the best available treatment are sold for extremely high prices. The order of magnitude is 100000 euros for a treatment. Zeuzem explained various aspects of the dynamics which has led to these prices and the circumstances under which they might be reduced in the future. In general this gave a rather depressing picture of the politics of health care relating to the approval and prescription of new drugs.

Let me get back to the scientific aspects of the theme, as explained by Bartenschlager. A obvious question to ask is: if hepatitis C can essentially be cured why does HIV remain essentially incurable despite the huge amount of effort and money spent on trying to find a treatment? The simple answer seems to be that HIV can hide while HCV cannot. Both these viruses have an RNA genome. Since the copying of RNA is relatively imprecise they both have a high mutation rate. This leads to a high potential for the development of drug resistance. This problem has nevertheless been overcome for HCV. Virus particles are continually being destroyed by the immune system and for the population to survive new virus particles must be produced in huge numbers. This is done by the liver cells. This heavy burden kills the liver cells after a while but the liver is capable of regenerating, i.e, replacing these cells. The liver has an impressive capability to survive this attack but every system has its limits and eventually, after twenty or thirty years, the long-term effects already mentioned develop. An essential difference between HIV and HCV is that the RNA of HCV can be directly read by ribosomes to produce viral proteins. By contrast, the RNA of HIV is used as a template to produce DNA by the enzyme reverse transcriptase and this DNA is integrated into the DNA of the cell. This integrated DNA (known as the provirus) may remain inactive, not leading to production of protein. As long as this is the case the virus is invisible to the immune system. This is one way the virus can hide. Moreover the cell can divide producing new cells also containing the provirus. There is also another problem. The main target of HIV are the T-helper cells. However the virus can also infect other cells such as macrophages or dendritic cells and the behaviour of the virus in these other cells is different from that in T-helper cells. It is natural that a treatment should be optimized for what happens in the typical host cell and this may be much less effective in the other cell types. This means that the other cells may serve as a reservoir for the virus in situations where the population is under heavy pressure from the immune system or drug treatment. This is a second sense in which the virus can hide.

Some of the recent drugs used to treat HCV are based on ideas developed for the treatment of HIV. For instance a drug of this kind may inhibit certain of the enzymes required for the reproduction of the virus. There is one highly effective drug in the case of HCV which works in a different way. The hepatitis C virus produces one protein which has no enzymatic activity and it is at first sight hard to see what use this could be for the virus. What it in fact does is to act as a kind of docking station which organizes proteins belonging to the cell into a factory for virus production.

The hepatitis C virus is a valuable example which illustrates the relations between various aspects of medical progress: improvement in scientific understanding, exploitation of that information for drug design, political problems encountered in getting an effective drug to the patients who need it. Despite the negative features which have been mentioned it is the subject of a remarkable success story.

### NFκB

May 1, 2016

NF$\kappa$B is a transcription factor, i.e. a protein which can bind to DNA and cause a particular gene to be read more or less often. This means that more or less of a certain protein is produced and this changes the behaviour of the cell. The full name of this transcription factor is ‘nuclear factor, $\kappa$-light chain enhancer of B cells’. The term ‘nuclear factor’ is clear. The substance is a transcription factor and to bind to DNA it has to enter the nucleus. NF$\kappa$B is found in a wide variety of different cells and its association with B cells is purely historical. It was found in the lab of David Baltimore during studies of the way in which B cells are activated. It remains to explain the $\kappa$. B cells produce antibodies each of which consists of two symmetrical halves. Each half consists of a light and a heavy chain. The light chain comes in two variants called $\kappa$ and $\lambda$. The choice which of these a cell uses seems to be fairly random. The work in the Baltimore lab had found out that NF$\kappa$B could skew the ratio. I found a video by Baltimore from 2001 about NF$\kappa$B. This is probably quite out of date by now but it contained one thing which I found interesting. Under certain circumstances it can happen that a constant stimulus causing activation of NF$\kappa$B leads to oscillations in the concentration. In the video the speaker mentions ‘odd oscillations’ and comments ‘but that’s for mathematicians to enjoy themselves’. It seems that he did not believe these oscillations to be biologically important. There are reasons to believe that they might be important and I will try to explain why. At the very least it will allow me to enjoy myself.

Let me explain the usual story about how NF$\kappa$B is activated. There are lots of animated videos on Youtube illustrating this but I prefer a description in words. Normally NF$\kappa$B is found in the cytosol bound to an inhibitor I$\kappa$B. Under certain circumstances a complex of proteins called IKK forms. The last K stands for kinase and IKK phosphorylates I$\kappa$B. This causes I$\kappa$B to be ubiquinated and thus marked for degradation (cf. the discussion of ubiquitin here). When it has been destroyed NF$\kappa$B is liberated, moves to the nucleus and binds to DNA. What are the circumstances mentioned above? There are many alternatives. For instance TNF$\alpha$ binds to its receptor, or something stimulates a toll-like receptor. The details are not important here. What is important is that there are many different signals which can lead to the activation of NF$\kappa$B. What genes does NF$\kappa$B bind to when it is activated? Here again there are many possibilities. Thus there is a kind of bow tie configuration where there are many inputs and many outputs which are connected to a single channel of communication. So how is it possible to arrange that when one input is applied, e.g. TNF$\alpha$ the right genes are switched on while another input activates other genes through the same mediator NF$\kappa$B? One possibility is cross-talk, i.e. that this signalling pathway interacts with others. If this cannot account for all the specificity then the remaining possibility is that information is encoded in the signal passing through NF$\kappa$B itself. For example, one stimulus could produce a constant response while another causes an oscillatory one. Or two stimuli could cause oscillatory responses with different frequencies. Evidently the presence of oscillations in the concentration of NF$\kappa$B presents an opportunity for encoding more information than would otherwise be possible. To what extent this really happens is something where I do not have an overview at the moment. I want to learn more. In any case, oscillations have been observed in the NF$\kappa$B system. The primary thing which has been observed to oscillate is the concentration of NF$\kappa$B in the nucleus. This oscillation is a consequence of the movement of the protein between the cytosol and the nucleus. There are various mathematical models for describing these oscillations. As usual in modelling phenomena in cell biology there are models which are very big and complicated. I find it particularly interesting when some of the observations can be explained by a simple model. This is the case for NF$\kappa$B where a three-dimensional model and an explanation of its relations to the more complicated models can be found in a paper by Krishna, Jensen and Sneppen (PNAS 103, 10840). In the three-dimensional model the unknowns are the concentrations of NF$\kappa$B in the nucleus, I$\kappa$B in the cytoplasm and mRNA coding for I$\kappa$B. The oscillations in normal cells are damped but sustained oscillations can be seen in mutated cells or corresponding models.

What is the function of NF$\kappa$B? The short answer is that it has many. On a broad level of description it plays a central role in the phenomenon of inflammation. In particular it leads to production of the cytokine IL-17 which in turn, among other things, stimulates the production of anti-microbial peptides. When these things are absent it leads to a serious immunodeficiency. In one variant of this there is a mutation in the gene coding for NEMO, which is one of the proteins making up IKK. A complete absence of NEMO is fatal before birth but people with a less severe mutation in the gene do occur. There are symptoms due to things which took place during the development of the embryo and also immunological problems, such as the inability to deal with certain bacteria. The gene for NEMO is on the X chromosome so that this disease is usually limited to boys. More details can be found in the book of Geha and Notarangelo mentioned in  a previous post.

### The German Dr. House

January 14, 2016

The central figure in the American TV series Dr. House is a doctor who is brilliant in the diagnosis of unusual medical conditions but personally very difficult. When I first saw this series I found the character so unpleasant that I did not want to watch the programme. However in the course of time I got drawn in to watching it by the interest of the medical content. While some aspects of this series are quite exaggerated and far from reality the medical parts are very accurate and well researched. As I learned yesterday even details seen there like the numbers on heart monitors accurately reflect the situation being portrayed. I have this information from a lecture I attended yesterday at the Medizinische Gesellschaft Mainz [Mainz Medical Society]. The speaker was Professor Jürgen Schäfer, a man who has become known in the media as the German Dr. House. I am pleased to report that I detected no trace of the social incompetence of Dr. House in Dr. Schäfer.

Jürgen Schäfer is trained as a cardiologist. He and his wife, who is a gastroenterologist, got so interested by the series Dr. House that they would spend time discussing the details of the diagnoses and researching the background after they has seen each programme. Then Schäfer had the idea that he could use Dr. House in his lectures at the University of Marburg. The first obstacle was to know if he could legally make use of this material. After a casual conversation with one of his patients who is a lawyer he contacted the necessary people and signed a suitable contract. At this time his project attracted considerable attention in the media even before it had started. In the lectures he analyses the cases occurring in the series. The students are encouraged to develop their own diagnoses in dialogue with the professor. These lectures are held in the evenings and are very popular with the students. In the evaluations the highest score was obtained for the statement that ‘the lectures are a lot of fun’.

This is only the start of the story. During a consultation in one of the episodes of Dr. House he suddenly makes a deep cut with a scalpel in the body of the patient (one of the melodramatic elements), opens the wound and shows that the flesh inside is black. The diagnosis is cobalt poisoning. After seeing this it occurred to Dr. Schäfer that this diagnosis might also apply to one of his own patients and this turned out to be true. In addition to serious heart problems this patient was becoming blind and deaf. He had had a hip joint replacement with an implant made of a ceramic material. At some point this became damaged and was replaced. In order to try to avoid the implant breaking again the new one was made of metal. The old implant fragmented and left splitters in the body. These had acted like sandpaper on the new joint and at the time of removal it had been reduced to 70% of its original size by this process. As a result large quantities of cobalt was released, resulting in the poisoning. The speaker showed a picture of the operation of another of his patients with a similar problem where the wound could be seen to be filled with a black oily liquid. Together with colleagues Schäfer published an account of this case in The Lancet with the title ‘Cobalt intoxication diagnosed with the help of Dr. House’. Not all his coauthors were happy with this title but Schäfer wanted to acknowledge his debt to the series. At the same time it was a great piece of advertizing for him which lead to a lot of attention in the international media.

Due to his growing fame Schäfer started to get a lot of letters from patients with mysterious illnesses. This was more than he could handle. He informed the administration of the university clinic where he worked that he was going to start sending back letters of this type unopened, since he just did not have the time to cope with them. To his surprise they wanted him to continue with this work and arranged from him to be relieved from other duties. They set up a new institute for him called Zentrum für unerkannte Krankheiten [centre for unrecognized diseases]. This was perhaps particularly surprising since this is a privately funded clinic and the work of this institute costs money rather than making money. The techniques used there include toxicological and genomic analyses.

Here is another example from the lecture. Schäfer’s institute uses large scale DNA analysis to screen for a broad range of parasites in patients with unclear symptoms. In one patient they found DNA of the parasite causing schistosomiasis. This disease is usually got by bathing in infected water in tropical or subtropical areas. The patient tested negatively for the parasite and had never been to a place where this disease occurs. The mystery was cleared up due to the help of a vet of Egyptian origin. He was familiar with schistosomiasis and due to his experience with large animals he was not afraid of analysing very large stool samples. He succeeded in finding eggs of the parasite in the patient’s stool. The diffculty was that the numbers of eggs were very low and that for certain reasons they were difficult to recognise in this case, except by an expert. The patient was treated for schistosomiasis as soon as the genetic results were available but it was very satisfying to have a confirmation by more classical techniques. The mystery of how the patient got infected was solved as follows. As a hobby he kept lots of fish and he imported these from tropical regions. The infection presumably came from the water in his aquarium. We see that in the modern world it is easy to import tropical diseases by express delivery after placing an order in the internet

I do not want to end before mentioning that Schäfer said something nice about how mathematicians can help medical doctors. He had a patient who is a mathematics professor and had the following problem. From time to time he would collapse and was temporarily paralysed although fully conscious. A possible explanation for this would have been an excessively high level of sodium in the body. On the other hand measurements showed that the concentration of sodium in his blood was normal, even after an attack. The patient then did a calculation (just simple arithmetic). On the basis of known data he worked out the amount of sodium and potassium in different types of food and noted a correlation between negative effects of a food on his health and the ratio of the sodium to potassium concentrations. This supported the hypothesis of sodium as a cause and encouraged the doctors to look more deeply into the matter. It turned out that in this type of disease the sodium is concentrated near the cell membrane and cannot be seen in the blood. A genetic analysis revealed that the patient had a mutation in a little-known sodium channel.

I think that this lecture was very entertaining for the audience, including my wife and myself. However this is not just entertainment. With his institute Schäfer is providing essential help for many people in very difficult situations. He has files of over 4000 patients. This kind of work requires a high investment in time and money which is not possible for a usual university clinic, not to mention an ordinary GP. It is nevertheless the case that Schäfer is developing resources which could be used more widely, such as standard protocols for assessing patients of this type. As he emphasized, while by definition a rare disease only effects a small number of patients the collection of all rare diseases together affects a large number of people. If more money was invested in this kind of research it could result in  a net saving for the health system since it would reduce the number of people running from one doctor to another since they do not have a diagnosis.

### David Vetter, the bubble boy

October 17, 2015

T cells are a class of white blood cells without which a human being usually cannot survive. An exception to this was David Vetter, a boy who lived 12 years without T cells. This was only possible because he lived all this time in a sterile environment, a plastic bubble. For this reason he became known as the bubble boy. The disease which he suffered from is called SCID, severe combined immunodeficiency, and it corresponds to having no T cells. The most common form of this is due to a mutation on the X chromosome and as a result it usually affects males. The effects set in a few months after birth. The mutation leads to a lack of the $\gamma$ chain of the IL-2 receptor. In fact this chain occurs in several cytokine receptors and is therefore called the ‘common chain’. Probably the key to the negative effects caused by its lack in SCID patients is the resulting lack of the receptor for IL-7, which is important for T cell development. SCID patients have a normal number of B cells but very few antibodies due to the lack of support by helper T cells. Thus in the end they lack both the immunity usually provided by T cells and that usually provided by B cells. This is the reason for the description ‘combined immunodeficiency’. I got the information on this theme which follows mainly from two sources. The first is a documentary film ‘Bodyshock – The Boy in the Bubble’ about David Vetter produced by Channel 4 and available on Youtube. (There are also less serious films on this subject, including one featuring John Travolta.) The second is the chapter on X-linked SCID in the book ‘Case Studies in Immunology’ by Raif Geha and Luigi Notarangelo. I find this book a wonderful resource for learning about immunology. It links general theory to the case history of specific patients.

At one point David started making punctures in his bubble as a way of attracting attention. Then it was explained to him what his situation was and why he must not damage the bubble. Later there was a kind of space suit produced for him by NASA which allowed him to move around outside his home. He only used it six times since he was too afraid there could be an accident. His physical health was good but understandably his psychological situation was difficult. New ideas in the practise of bone marrow transplantation indicated that it might be possible to use donors with a lesser degree of compatibility. On this basis David was given a transplant with his sister as the donor. It was not noticed that her bone marrow was infected with Epstein-Barr virus. As a result David got Burkitt’s lymphoma, a type of cancer which can be caused by that virus. (Compare what I wrote about this role of EBV here.) He died a few months after the operation, at the age of 12. Since that time treatment techniques have improved. The patient whose case is described in the book of Geha and Notarangelo had a successful bone marrow transplant (with his mother as donor). Unfortunately his lack of antibodies was not cured but this can be controlled with injections of immunoglobulin once every three weeks.

### Immunotherapy for cancer

September 20, 2015

A promising innovative approach to cancer therapy is to try to persuade the immune system to attack cancer cells effectively. The immune system does kill cancer cells and presumably removes many tumours which we never suspect we had. At the same time established tumours are able to successfully resist this type of attack in many cases. The idea of taking advantage of the immune system in this way is an old one but it took a long time before it became successful enough to reach the stage of an approved drug. This goal was achieved with the approval of ipilimumab for the treatment of melanoma by the FDA in 2011. This drug is a monoclonal antibody which binds the molecule CTLA4 occurring on the surface of T cells.

To explain the background to this treatment I first recall some facts about T cells. T cells are white blood cells which recognize foreign substances (antigens) in the body. The antigen binds to a molecule called the T cell receptor on the surface of the cell and this gives the T cell an activation signal. Since an inappropriate activation of the immune system could be very harmful there are built-in safety mechanisms. In order to be effective the primary activation signal has to be delivered together with a kind of certificate that action is really necessary. This is a second signal which is given via another surface molecule on the T cell, CD28. The T cell receptor only binds to an antigen when the latter is presented on the surface of another cell (an antigen-presenting cell, APC) in a groove within another molecule, an MHC molecule (major histocompatibility complex). On the surface of the APC there are under appropriate circumstances other molecules called B7.1 and B7.2 which can bind to CD28 and give the second signal. Once this has happened the activated T cell takes appropriate action. What this is depends on the type of T cell involved but for a cytotoxic T cell (one which carries the surface molecule CD8) it means that the T cell kills cells presenting the antigen. If the cell was a virus-infected cell and the antigen is derived from the virus then this is exactly what is desired. Coming back to the safety mechanisms, it is not only important that the T cell is not erroneously switched on. It is also important that when it is switched on in a justified case it should also be switched off after a certain time. Having it switched on for an unlimited time would never be justified. This is where CTLA4 comes in. This protein can bind to B7.1 and B7.2 and in fact does so more strongly than CD28. Thus it can crowd out CD28 and switch off the second signal. By binding to CTLA4 the antibody in ipilimumab stops it from binding to B7.1 and B7.2, thus leaving the activated T cell switched on. In some cases cancer cells present unusual antigens and become a target for T cells. The killing of these cells can be increased by CTLA4 via the mechanism just explained. At this point I should say that it may not be quite clear whether this is really the mechanism of action of CTLA4 in causing tumours to shrink. Alternative possibilities are mentioned in the Wikipedia article on CTLA4.

There are various things which have contributed to my interest in this subject. One is lectures I heard in the series ‘Universität im Rathaus’ [University in the Town Hall] in Mainz last February. The speakers were Matthias Theobald and Ugur Sahin and the theme was personalized cancer medicine. The central theme of what they were talking about is one step beyond what I have just sketched. A weakness of the therapy using antibodies to CTLA4 or the related approach using antibodies to another molecule PD-1 is that they are unspecific. In other words they lead to an increase not only in the activity of the T cells specific to cancer cells but of all T cells which have been activated by some antigen. This means that serious side effects are very likely. An approach which is theoretically better but as yet in a relatively early stage of development is to produce T cells which are specific for antigens belonging to the tumour of a specific patient and for an MHC molecule of that patient capable of presenting that antigen. From the talk I had the impression that doing this requires a lot of input from bioinformatics but I was not able to understand what kind of input it is. I would like to know more about that. Coming back to CTLA4, I have been interested for some time in modelling the activation of T cells and in that context it would be natural to think about also modelling the deactivating effects of CTLA4 or PD-1. I do not know whether this has been tried.

### 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.