## Archive for the ‘immunology’ Category

### The importance of dendritic cells

October 30, 2016

I just realized that something I wrote in a previous post does not make logical sense. This was not just due to a gap in my exposition but to a gap in my understanding. I now want to correct it. A good source for the correct story is a video by Ira Mellman of Genentech. I first recall some standard things about antigen presentation. In this process peptides are presented on the surface of cells with MHC molecules which are of two types I and II. MHC Class I molecules are found on essentially all cells and can present proteins coming from viruses infecting the cell concerned. MHC Class II molecules are found only on special cells called professional antigen presenting cells. These are macrophages, T cells and dendritic cells. The champions in antigen presentations are the dendritic cells and those are the ones I will be talking about here. In order for a T cell to be activated it needs two signals. The first comes through the T cell receptor interacting with the peptide-MHC complex on an APC. The second comes from CD28 on the T cell surface interacting with B7.1 and B7.2 on the APC.

Consider now an ordinary cell, not an APC, which is infected with a virus. This could, for instance be an epithelial cell infected with a influenza virus. This cell will present peptides derived from the virus with MHC Class I molecules. These can be recognized by activated ${\rm CD8}^+$ T cells which can then kill the epithelial cell and put an end to the viral reproduction in that cell. The way I put it in the previous post it looked like the T cell could be activated by the antigen presented on the target cell with the help of CD28 stimulation. The problem is that the cell presenting the antigen in this case is an amateur. It has no B7.1 or B7.2 and so cannot signal through CD28. The real story is more complicated. The fact is that dendritic cells can also present antigen on MHC Class I, including peptides which are external to their own function. A possible mechanism explained in the video of Mellman (I do not know if it is certain whether this is the mechanism, or whether it is the only one) is that a cell infected by a virus is ingested by a dendritic cell by phagocytosis, so that proteins which were outside the dendritic cell are now inside and can be brought into the pathway of MHC Class I presentation. This process is known as cross presentation. Dendritic cells also have tools of the innate immune system, such as toll-like receptors, at their disposal. When they recognise the presence of a virus by these means they upregulate B7.1 and B7.2 and are then in a position to activate ${\rm CD8}^+$ T cells. Note that in this case the virus will be inside the dendritic cell but not infecting it. There are viruses which use dendritic cells for their own purposes, reproducing there or hitching a lift to the lymph nodes where they can infect their favourite cells. An example is HIV. The main receptor used by this virus to enter the cells is CD4 and this is present not only on T cells but also on dendritic cells. Another interesting side issue is that dendritic cells can not only activate T cells but also influence the differentiation of these cells into various different types. The reason is that the detection instruments of the dendritic cell not only recognise that a pathogen is there but can also classify it to some extent (Mellman talks about a bar code). Based on this information the dendritic cell secretes various cytokines which influence the differentiation process. For instance they can influence whether a T-helper cell becomes of type Th1 or Th2. This is related to work which I did quite a long time ago on an ODE system modelling the interactions of T cells and macrophages. In view of what I just said it ḿight be interesting to study an inhomogeneous version of this system. The idea is to include an external input of cytokines coming from dendritic cells. In fact the unknowns in the system are not the concentrations of cytokines but the populations of cells. Thus it would be appropriate to introduce an inhomogeneous contribution into the terms describing the production of different types of cells.

### 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.

### In the beginning was the worm

September 29, 2016

In a previous post I mentioned the book by Andrew Brown whose title I have used here. I came across it in a second hand bookshop in Berkeley when I was spending time at MSRI in 2009. I read it with pleasure then and now I have read it again. It contains the story of how the worm Caenorhabditis elegans became an important model organism. This came about because Sydney Brenner deliberately searched for an organism with favourable properties and promoted it very effectively once he had found it. It is transparent so that it is possible to see what is going on inside it and it is easy to keep in the lab and reproduces fast enough in order to allow genetic research to be done rapidly. The organism sought was supposed to have a suitable sexual system. C. elegans is normally hermaphrodite but does also have males and so it is acceptable from that point of view. One further important fact about C. elegans is that it has a nervous system, albeit a relatively simple one. (More precisely, it has two nervous systems but I have not looked into the details of that issue.) Brenner was looking to understand how genetics determines behaviour and C. elegans gave him an opportunity to make an attack on this problem in two steps. First understand how to get from genes to neurons and then understand how to get from neurons to behaviour. C. elegans has a total of 302 neurons. It has 959 cells in total, not including eggs and sperm. Among the remarkable things known about the worm are the complete developmental history of each of its cells and the wiring diagram of its neurons. There are about 6400 synapses but the exact number, unlike the number of cells or neurons, is dependent on the individual. For orientation note that C. elegans is a eukaryotic organism (in contrast to phages or E. coli) which is multicellular (in contrast to Saccharomyces cerevisiae) and it is an animal (in contrast to Arabidopsis thaliana). Otherwise, among the class of model organisms, it is as simple and fast reproducing as possible. In particular it is simpler than Drosophila, which was traditionally the favourite multicellular model organism of the geneticists.

In this blog I have previously mentioned Sydney Brenner and expressed my admiration for him. I have twice met him personally when he was giving talks in Berlin and I have also watched a number of videos of him which are available on the web and read various texts he has written. In this way I have experienced a little of the magnetism which allowed him to inspire gifted and risk-taking young scientists to work on the worm. Brenner spent 20 years at the Laboratory of Molecular Biology in Cambridge, a large part of it as director of that organization. In the pioneering days of molecular biology the lab was producing Nobel prizes in series. He had to wait until 2002 for his own Nobel prize (for physiology or medicine), shared with John Sulston and Robert Horvitz. In his Nobel speech Brenner said that he felt there was a fourth prizewinner, C. elegans, which, however, did not get a share of the money. My other favourite quote from that speech is his description of the (then) present state of molecular biology, ‘drowning in a sea of data, starving for knowledge’. Since then that problem has only got worse.

Now I will collect some ‘firsts’ associated with C. elegans. It was the first multicellular organism to have its whole genome sequenced, in 1998. This can also be seen as the point of departure for the human genome project. Here the worm people overtook the drosophilists and the Drosophila genome was only finished in 2000. Sulston played a central role in the public project to sequence the human genome and the struggle with the commercial project of Craig Venter. It was only the link between the worm genome project and the human one which allowed enough money to be raised to finish the worm sequence. According to the book Sulston was more interested in the worm project since he wanted to properly finish what he had started. Martin Chalfie, coming from the worm community introduced GFP (green fluorescent protein) into molecular biology. He first expressed it in E. coli and C. elegans. He got a Nobel prize for that in 2008. microRNA (miRNA) was first found in C. elegans. It is the basis of RNA interference (RNAi), also first found in C. elegans. This earned a Nobel prize in 2006. The genetics of the process of apoptosis (programmed cell death) was understood by studying C. elegans. When Sulston was investigated the cell lineage he saw that certain cells had to die as part of the developmental process. Exactly 131 cells die during this process.

To conclude I mention a couple of features of C. elegans going beyond the time covered by the book. I asked myself what we can learn about the immune system from C. elegans. Presumably every living organism needs an immune system to survive in a hostile environment. The adaptive immune system in the form known in humans only exists in vertebrates and hence, in particular, not in the worm. Some related comments can be found here. It seems that C. elegans has no adaptive immune system at all but it does have innate immunity. It has cells called coelomocytes which have at least some resemblance to immune cells. It has six of them in total. Compare this with more than $10^9$ immune cells per litre in our blood. C. elegans eats bacteria. These days the human gut flora is a fashionable topic. A couple of weeks ago I heard a talk by Giulia Enders, the author of the book ‘Darm mit Charme’ which sold a million copies in 2014. I had bought and read the book and found it interesting although I was not really enthusiastic about it. Now TV advertising includes products aimed at the gut flora of cats. So what about C. elegans? Does it have an interesting gut flora? The answer seems to be yes. See for instance the 2013 article ‘Worms need microbes too’ in EMBO Mol. Med. 5, 1300.

### ECMTB 2016 in Nottingham

July 17, 2016

This past week I attended a conference of the ESMTB and the SMB in Nottingham. My accomodation was in a hall of residence on the campus and my plan was to take a tram from the train station. When I arrived it turned out that the trams were not running. I did not find out the exact reason but it seemed that it was a problem which would not be solved quickly. Instead of finding out what bus I should take and where I should take it from I checked out the possibility of walking. As it turned out it was neither unreasonably far nor complicated. Thus, following my vocation as pedestrian, I walked there.

Among the plenary talks at the conference was one by Hisashi Ohtsuki on the evolution of social norms. Although I am a great believer in the application of mathematics to many real world problems I do become a bit sceptical when the area of application goes in the direction of sociology or psychology. Accordingly I went to the talk with rather negative expectations but I was pleasantly surprised. The speaker explained how he has been able to apply evolutionary game theory to obtain insights into the evolution of cooperation in human societies under the influence of indirect reciprocity. This means that instead of the simple direct pattern ‘A helps B and thus motivates B to help A’ we have ‘C sees A helping B and hence decides to help A’ and variations on that pattern. The central idea of the work is to compare many different strategies in the context of a mathematical model and thus obtain ideas about what are the important mechanisms at work. My impression was that this is a case where mathematics has generated helpful ideas in understanding the phenomenon and that there remain a lot of interesting things to be done in that direction. It also made me reflect on my own personal strategies when interacting with other people. Apart from the interesting content the talk was also made more interesting by the speaker’s entertaining accounts of experiments which have been done to compare with the results of the modelling. During the talk the speaker mentioned self-referentially that the fact of his standing in front of us giving the talk was an example of the process of the formation of a reputation being described in the talk. As far as I am concerned he succeeded in creating a positive reputation both for himself and for his field.

Apart from this the other plenary talk which I found most interesting was by Johan van de Koppel. He was talking about pattern formation in ecology and, in particular, about his own work on pattern formation in mussel beds. A talk which I liked much less was that of Adelia Sequeira and it is perhaps interesting to ask why. She was talking about modelling of atherosclerosis. She made the valid point near the beginning of her lecture that while heart disease is a health problem of comparable importance to cancer in the developed world the latter theme was represented much more strongly than the former at the conference. For me cancer is simply much more interesting than heart disease and this point of view is maybe more widespread. What could be the reason? One possibility is that the study of cancer involves many more conceptual aspects than that of heart disease and that this is attractive for mathematicians. Another could be that I am a lot more afraid of being diagnosed with cancer some day than of being diagnosed with heart disease although the latter may be no less probable and not less deadly if it happens. To come back to the talk I found that the material was too abundant and too technical and that many ideas were used without really being introduced. The consequence of these factors was that I lost interest and had difficulty not falling asleep.

In the case of the parallel talks there were seventeen sessions in parallel and I generally decided to go to whole sessions rather than trying to go to individual talks. I will make some remarks about some of the things I heard there. I found the first session I went to, on tumour-immune dynamics, rather disappointing but the last talk in the session, by Shalla Hanson was a notable exception. The subject was CAR T-cells and what mathematical modelling might contribute to improving therapy. I found both the content and the presentation excellent. The presentation packed in a lot of material but rather than being overwhelmed I found myself waiting eagerly for what would come next. During the talk I thought of a couple of questions which I might ask at the end but they were answered in due course during the lecture. It is a quality I admire in a speaker to be able to anticipate the questions which the audience may ask and answer them. I see this less as a matter of understanding the psychology of the audience (which can sometimes be important) and rather of really having got to the heart of the subject being described. There was a session on mathematical pharmacology which I found interesting, in particular the talks of Tom Snowden on systems pharmacology and that of Wilhelm Huisinga on multidrug therapies for HIV. In a session on mathematical and systems immunology Grant Lythe discussed the fascinating question of how to estimate the number of T cell clones in the body and what mathematics can contribute to this beyond just analysing the data statistically. I enjoyed the session on virus dynamics, particularly a talk by Harel Dahari on hepatitis C. In particular he told a story in which he was involved in curing one exceptional HCV patient with a one-off therapy using a substance called silibinin and real-time mathematical modelling.

I myself gave a talk about dinosaurs. Since this is work which is at a relatively early stage I will leave describing more details of it in this blog to a later date.

### 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.

### 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.

### Trip to the US

October 5, 2015

Last week I visited a few places in the US. My first stop was Morgantown, West Virginia where my host was Casian Pantea. There I had a lot of discussions with Casian and Carsten Conradi on chemical reaction network theory. This synergized well with the work I have recently been doing preparing a lecture course on that subject which I will be giving in the next semester. I gave a talk on MAPK and got some feedback on that. It rained a lot and there was not much opportunity to do anything except work. One day on the way to dinner while it was relatively dry I saw a Cardinal and I fortunately did have my binoculars with me. On Wednesday afternoon I travelled to New Brunswick and spent most of Thursday talking to Eduardo Sontag at Rutgers. It was a great pleasure to talk to an excellent mathematician who also knows a lot about immunology. He and I have a lot of common interests which is in part due to the fact that I was inspired by several of his papers during the time I was getting into mathematical biology. I also had the opportunity to meet Evgeni Nikolaev who told me a variety of interesting things. They concerned bifurcation theory in general, its applications to the kinds of biological models I am interested in and his successes in applying mathematical models to understanding concrete problems in biomedical research such as the processes taking place in tuberculosis. My personal dream is to see a real coming together of mathematics and immunology and that I have the chance to make a contribution to that process.

On Friday I flew to Chicago in order to attend an AMS sectional meeting. I had been in Chicago once before but that is many years ago now. I do remember being impressed by how much Lake Michigan looks like the sea, I suppose due to the structure of the waves. This impression was even stronger this time since there were strong winds whipping up the waves. Loyola University, the site of the meeting, is right beside the lake and it felt like home for me due to the combination of wind, waves and gulls. The majority of those were Ring-Billed Gulls which made it clear which side of the Atlantic I was on. There were also some Herring Gulls and although they might have been split from those on the other side of the Atlantic by the taxonomists I did not notice any difference. It was the first time I had been at an AMS sectional meeting and my impression was that the parallel sessions were very parallel, in other words in no danger of meeting. Most of the people in our session were people I knew from the conferences I attended in Charlotte and in Copenhagen although I did make a couple of new acquaintances, improving my coverage of the reaction network community.

In a previous post I mentioned Gheorghe Craciun’s ideas about giving the deficiency of a reaction network a geometric interpretation, following a talk of his in Copenhagen. Although I asked him questions about this on that occasion I did not completely understand the idea. Correspondingly my discussion of the point here in my blog was quite incomplete. Now I talked to him again and I believe I have finally got the point. Consider first a network with a single linkage class. The complexes of the network define points in the species space whose coordinates are the stoichiometric coefficients. The reactions define oriented segments joining the educt complex to the product complex of each reaction. The stoichiometric subspace is the vector space spanned by the differences of the complexes. It can also be considered as a translate of the affine subspace spanned by the complexes themselves. This makes it clear that its dimension $s$ is at most $n-1$, where $n$ is the number of complexes. The number $s$ is the rank of the stoichiometric matrix. The deficiency is $n-1-s$. At the same time $s\le m$. If there are several linkage classes then the whole space has dimension at most $n-l$, where $l$ is the number of linkage classes. The deficiency is $n-l-s$. If the spaces corresponding to the individual linkage classes have the maximal dimension allowed by the number of complexes in that class and these spaces are linearly independent then the deficiency is zero. Thus we see that the deficiency is the extent to which the complexes fail to be in general position. If the species and the number of complexes have been fixed then deficiency zero is seen to be a generic condition. On the other hand fixing the species and adding more complexes will destroy the deficiency zero condition since then we are in the case $n-l>m$ so that the possibility of general position is excluded. The advantage of having this geometric picture is that it can often be used to read off the deficiency directly from the network. It might also be used to aid in constructing networks with a desired deficiency.

### 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.

### Itk and T cell signalling

June 18, 2014

I have spent a lot of time thinking about signalling pathways involved in the activation of T cells and ways in which mathematical modelling could help to understand them better. In the recent past I had not found much time to read about the biological background in this area. Last weekend I started doing this again. In this context I remembered that Al Singer told me that Itk was an interesting target for modelling. At that time I knew nothing about Itk and only now have I come back to that, reading a review article by Andreotti et. al. in Cold Spring Harbor Perspectives in Biology, 2010. Before I say more about that I will collect some more general remarks.

The signalling network involved in the activation of T cells is very complex but over time I have become increasingly familiar with it. I want to review now some of the typical features to be found in this and related networks. Phosphorylation and dephosphorylation play a very important role. Phosphate groups can be added to or removed from many proteins, replacing (in animals) the hydroxyl groups in the side chains of the amino acids serine, threonine and tyrosine. The enzymes which add and remove these groups are the kinases and phosphatases, respectively. Often the effect of (de-)phosphorylation is to switch the kinase or phosphatase activity of the protein on or off. This kind of process has been studied from a mathematical point of view relatively frequently, with the MAPK cascade being a popular example. Another phenomenon which is controlled by phosphorylation is the binding of one protein to another, for instance via SH2 domains. An example involved in T cell activation is the binding of ZAP-70 to the $\zeta$-chain associated to the T cell receptor. This binding means that certain proteins are brought into proximity with each other and are more likely to interact. Another type of players are linker or adaptor proteins which seem to have the main (or exclusive?) function of organising proteins spatially. One of these I was aware of is LAT (linker of activated T cells). While reading the Itk paper I came across Slp76, which did not strike me as familiar. Another element of signalling pathways is when one protein cleaves another. This is for instance a widespread mechanism in the complement system.

Now back to Itk (IL2-inducible T cell kinase). It is a kinase and belongs to a family called the Tec kinases. Another member of the family which is more prominent medically is Btk, which is important for the function of B cells. Mutations in Btk cause the immunodeficiency disease X-linked agammaglobulinemia. This is the subject of the first chapter of the fascinating book ‘Case studies in Immunology’ by Geha and Notarangelo. As the name suggests this gene is on the X chromosome and correspondingly the disease mainly affects males. In some work I did I looked at the pathway leading to the transcription factor NFAT. However I only looked at the more downstream part of the pathway. This is related to the fact that in experimental work the more upstream part is often bypassed by the use of ionomycin. This substance causes a calcium influx into the cytosol which triggers the lower part of the pathway. In the natural situation the calcium influx is caused by ${\rm IP}_3$ binding to receptors on the endoplasmic reticulum. The ${\rm IP}_3$ comes from the cleavage of ${\rm PIP}_2$ by ${\rm PLC}\gamma$. This I knew before, but what comes before that? In fact ${\rm PLC}\gamma$ is activated through phosphorylation by Itk and Itk is activated through phosphorylation by Lck, a protein I was very familar with due to some of its other effects in T cell activation.

It seems that in knockout mice which lack Itk T cell development is still possible but the immune system is seriously compromised. Effects can be seen in the differentiation of T-helper cells into the types Th1, Th2 and Th17. The problems are less in the case of Th1 responses because Itk can be replaced by another Tec kinase called Rlk. In the case of Th2 responses this does not work and the secretion of the typical Th2 cytokine IL4 is seriuously affected. The Th17 cells are in an intermediate position, with IL17A being affected but IL17F not. Itk also has important effects during the maturation of T cells. Despite the many roles of Itk there are few cases known where mutations in the corresponding genes leads to medical problems in humans. This kind of mutation is a unique opportunity to learn about the role of various substances in humans, where direct experiments are not possible.

In a 2009 paper of Huck et. al. (J. Exp. Med. 119, 1350) the case of two sisters who suffered from serious problems with immunity is described. In particular they had strong infections with Epstein-Barr virus which could not be overcome despite intensive treatment. They also has an excess of B cells. The older sister died at the age of ten. The younger sister was even more severely affected and stem cell transplantation was attempted when she was six years old. Unfortunately she did not survive that. After extensive investigations it was discovered that both sisters were homozygous for the same mutation in the gene for Itk and that was the source of their problems. Their medical history offers clues to what Itk does in humans. The gene is on chromosome 5 and thus it is natural that its mutations are much more rarely discovered than those of Btk. The mutation must occur in both copies of the gene in order to have a serious effect and this can happen just as easily in females as in males.

### Guillain-Barré syndrome

May 9, 2013

Yesterday I went to a talk by Hans-Peter Hartung about autoimmune diseases of the peripheral nervous system. To start with he gave a summary of similarities and differences between the peripheral and central nervous systems and their relations to the immune system. Of the diseases he later discussed one which played a central role was Guillain-Barré syndrome. In fact he emphasized that this ‘syndrome’ is phenomenologically defined and consists of several diseases with different underlying mechanisms. There is one form which is sporadic in its occurrence and predominant in the western world and another which can take an epidemic form and occurs in China. At a time when medical services in China were very poor this kind of epidemic had very grave consequences. Now, however, I want to return to the ‘classical’ form of Guillain-Barré.

GBS is a disease which is fascinating for the outside observer and no doubt terrifying for the person affected by it. I first learned about it in an account – I do not remember where I read it – of the case of a German doctor. He was on holiday in Tenerife when he fell ill. He recognized the characteristic pattern of symptoms, suspected GBS and got on the first plane home. He wanted to optimize the treatment he got by going to the best medical centre he knew to get treated. The treatment was successful. In GBS the immune system attacks peripheral nerves and this leads to a rapidly progressive paralysis over the course of a few days. In a significant proportion of patients this leads to the control of the muscles responsible for breathing failing and thus to death. For this reason it it is important for the patient to quickly reach a place where the disease will be recognized and they can be put on a ventilator when needed.The disease can then also be treated by plasmapheresis or immunoglobulins. In the talk it was mentioned that in the epidemics in China it was often necessary to put patients on a manual ventilator which was operated their relatives. If this acute phase can be overcome the patient usually recovers rather completely, although some people have lasting damage. It is typical that in a single patient the disease does not recur although there are a small number of cases where there are several relapses and disability accumulates.

It has been suggested that influenza infections, or influenza vaccinations, can lead to an increased risk of developing GBS. This has been an important element of controversies surrounding vaccinations, including those against H1N1. I wrote briefly about this in a previous post. In the talk the speaker mentioned a recent Canadian study indicating a slight risk of GBS due to vaccination against influenza. Nevertheless this risk was still a lot less than that due to actually becoming infected with influenza. There has also been a German study with similar results which, however, has not yet been published. There is another kind of infection which appears to carry a much higher risk, namely that with the bacterium Campylobacter jejuni. I actually mentioned this in my previous post but had completely forgotten about it. In the talk it was pointed out that this infection is quite common while GBS is very rare. So the question arises of why GBS is not more frequent. A possible explanation is that the bacterium is rather variable. The suggested mechanism is molecular mimicry (and it seems that GBS is the first case where molecular mimicry was precisely documented). In other words, certain molecules of the bacterium are similar to molecules belonging to the nervous system. Then it happens that antibodies against the bacterium cause damage to the nerves. Depending on the variant of the bacterium this similarity of the two types of molecules is more or less strong so that the effect is more or less pronounced. There is some idea in this case what exactly the molecules are which show this similarity. They are so-called gangliosides, a type of glycolipids.

This has reminded me of an issue which fascinated me before. Is there a simple explanation of why some autoimmune diseases show repeated relapses while others show a single episode (like typical GBS), a continuous progression or a combination of relapsing and progressive phases at different times? Has anyone collected data on these patterns over a variety of autoimmune diseases?