Archive for the ‘immunology’ Category

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.

David Vetter had an older brother who also suffered from SCID and died of infection very young. Thus his parents and their doctors were warned. The brother was given a bone marrow transplant from his sister, who had the necessary tissue compatibility. Unfortunately this did not save him, presumably because he had already been exposed to too many infections by the time it was carried out. The parents decided to have another child, knowing that if it was a boy the chances of another case of SCID were 50%. Their doctors had a hope of being able to save the life of such a child by isolating him and then giving him a bone marrow transplant before he had been exposed to infections. The parents very soon had another child, it was a boy, he had SCID. The child was put into a sterile plastic bubble immediately after birth. Unfortunately it turned out that the planned bone marrow donor, David’s sister, was not a good match for him. It was necessary to wait and hope for an alternative donor. This hope was not fulfilled and David had to stay in the bubble. This had not been planned and it must be asked whether the doctors involved had really thought through what would happen if the optimal variant they had thought of did not work out.

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?

Hello Mainz

April 18, 2013

This post is in some sense dual to the earlier one ‘goodbye to Berlin‘. To start with I can confirm that there is no shortage of Carrion Crows (and no Hooded Crows) in Mainz. When I arrived here and was waiting for my landlord to come and let me into my flat I saw some small and intensely green spots of colour in a row of trees in front of me. I knew the source of these – they were what I could see of Ring-Necked Parakeets. I have known for a long time that these birds live wild in England but it was only relatively recently, in the course of my activity looking for jobs, that I realised they were so common in parts of Germany. While in Heidelberg for an interview I observed a big number of them making a lot of noise in a small wood opposite the main railway station. I also saw some of them when I came to Mainz for the interview which eventually led to my present job. In my old institute in Golm I often used to see Red Kites out of my office window. It occurred to me that these might be replaced by Black Kites in Mainz. During my first weekend here I was walking across the campus of the university when I saw a large and unfamiliar bird of prey approaching me. When it came closer I realised that it was a Black Kite. I enjoyed the encounter. Since that I have also seen one from my office window. The Red Kite is a beautiful bird but for some reason I feel closer to its dark relative. It gives me a feeling of the south since the first place I saw these birds many years ago was in the Camargue.

Eva and I have been using Skype to maintain contact. I feel that this big change in our life has not been without benefits for our communication with each other and when I was home last weekend it was a richer experience than many weekends in the last few years. I appreciate the warm welcome I have had from my colleagues here in Mainz and my first days here, while sometimes a bit hectic, have been rewarding. Breaking the routine of years opens up new possibilities. I assured myself that I will not completely have to do without interesting biological talks here by going to a lecture by Alexander Steinkasserer on CD83. This taught me some more about dendritic cells for which this surface molecule is an important marker.

This is the first week of lectures here and yesterday brought the first concrete example of the new direction in my academic interests influencing my teaching, with the start of my seminar on ‘ordinary differential equations in biology and chemistry’. The first talk was on Lotka-Volterra equations. The subjects to be treated by other students in later lectures include ones a lot further from classical topics.

Talk on mathematical modelling in Karlstad

November 20, 2012

Yesterday I was in Karlstad in Sweden to give a talk on the uses of mathematical modelling in the natural sciences. I was invited to do this by Claes Uggla and I was very happy to have the opportunity to present some of my ideas on this subject. The talk was structured as a series of examples involving applications of different mathematical techniques. Many of these examples have been discussed in some form in this blog during the past few years and indeed a lot of my ideas on the subject were developed in conjunction with the blog posts. The subjects were William Harvey and the circulation of the blood, multidrug therapy for HIV-AIDS, the lizard Uta stansburiana, oscillations near the big bang, Liesegang rings, modelling oscillations in vole populations using a reaction-diffusion system, signal transduction in T cells.

As well as presenting a variety of applications of different types of mathematics I also wanted to explain some mathematical connections between these subjects. One central idea is that structural stability is an issue of key importance in modelling natural phenomena. Most phenomenological models involve parameters or other elements which are not known exactly. Thus to be of interest for applications features of the dynamics of the model should be invariant under arbitrary small perturbations of the system. More precisely, if a model does not possess an invariance of this type but is nevertheless useful this requires some explanation. One possible source of an explanation is the presence of what I call ‘absolute elements’ in the model. For instance, in population dynamics if a population is zero at some time then it will definitely remain zero. This fact is independent of the details of how the population grows when it is non-zero. Similarly a spacetime singularity can define an absolute element in cosmology. When the spacetime metric breaks down this ends the dynamics in a way which is independent of the details of the dynamics of the matter away from the singularity. Thus structural stability can be weakened to the condition of invariance under small perturbations which leave certain submanifolds fixed. This can lead to the appearance of relevant heteroclinic cycles although these are not structurally stable in the absolute sense. It explains the appearance of heteroclinic cycles in the models for lizards and for the big bang in a unified way. In a similar way, restricting the perturbations of a system of chemical reactions to those which leave a particular reaction irreversible can furnish the homoclinic orbit needed to model Liesegang rings.

I have now put a slightly extended version of this talk with references on my web page. On the same day there was a talk by Bernt Wennberg on models for the collective motion of birds and fish, concentrating mainly on kinetic models related to the Boltzmann equation. At the start of his talk he showed some of the well-known pictures of flocks of Starlings over Rome. In the evening I had my own pleasant experience with a flock of birds. A large number of Jackdaws (a couple of hundred) were flying around the central square in Karlstad and calling. For some reason I have become increasingly attached to the Jackdaw over the years. At this point, and without a good excuse, I want to tell a story about Jackdaws from the book ‘King Solomon’s Ring’ by Konrad Lorenz. It is a long time since I read the book and so I hope I do not distort the story too much. At one time Lorenz was living in a small village in Austria where he was regarded by the locals as a bit crazy. One of his interests was the social life of Jackdaws. There were Jackdaws living on the roofs of the houses and he climbed up to get close to them. In order to fit in better with his black subjects he decided to dress in black. The only ‘suitable’ black clothing he could find was a devil’s costume left over from a fancy dress party. No doubt the spectacle of him climbing over the roofs dressed as the devil perfected his reputation with the local inhabitants.

Conference on systems biology of T cells in Baeza, part 2

October 25, 2012

In the remaining one and a half days of the conference there were another fourteen talks and I will mention some aspects of their contents which attracted my attention. One recurring theme was that the encounter of a T cell receptor (TCR) with the peptide it recognizes bound to an MHC molelcule (pMHC) is often not just the encounter of one TCR with one pMHC but of multiple players. It can be shown by electron microscopy that the TCR tend to cluster on the surface of a T cell even before it has encountered antigen. This is done by attaching gold particles to the TCR so that they show up as black dots on the electron micrograph. It was shown in the talk of Hisse van Santen that a similar thing happens with the pMHC on the surface of antigen presenting cells. Judging from the discussion after the talk it seems that the explanation for this is that the pMHC, which are well known to be produced in the interior of the cell, are exported to the surface in groups. There also seems to be a widely held opinion that signalling through the T cell receptor is absolutely dependent on clustering of TCR. This makes life more complicated than it otherwise might have been. I learned at this conference that experiments on T cell signalling in vitro are often done by using tetramers, i.e. groups of four pMHC which are bound together covalently. In the talk of Wolfgang Schamel described experiments using tetramer binding. He said that this work was linked with some mathematical modelling, done by Thomas Höfer and others, but he did not want to take questions on that. My impression was that the model was an extension of the kinetic proofreading model. It has not yet been published and so I did not yet have an opportunity to look at it. Carmen Molina-París and Balbino Alarcón discussed cooperative effects in T cell receptor binding.

Michal Polonsky showed pictures of individual T cells trapped in small wells in a microfluidic device. When activated they wriggle very vigorously. These are the kind of pictures which could easily make you take a very anthropomorphic view of T cells. The aim of this work is to observe the differentiation, division and death of the cells over long periods (several days). If they were not trapped it would be extremely difficult to follow them under the microscope since they would be liable to run away. A break from the purely scientific talks was provided by a presentation of Dinah Singer about the systems biology programme at the National Cancer Institute in the US, a programme which she runs. Apart from concrete information about funding another aspect of this was the question of what might be learned about the potential for applying systems biology to immunology from existing applications of these ideas to cancer research. Dipankar Nandi talked about a phenomenon I had never heard of before and would never have expected – atrophy of the thymus as a consequence of certain diseases. Finally, I was on more familiar ground with the talk of Isabel Mérida about certain signalling pathways in T cell activation. The substance at the centre of her talk, diacylglycerol kinase, was not familiar to me but the context was. Right at the end of the conference there was a general discussion session planned. This session, which was led by Ed Palmer, ended up being very short. This was due to the (in itself positive) fact that the discussions after (and during) the individual talks had taken up more time than planned. The final discussion was interesting despite its brevity. The basic theme was: if mathematicians are collaborating with immunologists what can each side do to help the other in this process? Interesting points were brought up and we were all sent home with some things to think about.

Conference on systems biology of T cells in Baeza

October 22, 2012

At the moment I am attending a conference on systems biology of T cells in Baeza. Of the eleven talks today the first nine made no mention of mathematics – there was not a single equation. The tenth, by Zvi Grossmann, did show a couple. Thus the bias today was very much towards experimental immunology. It was interesting for me to be immersed in this atmosphere and I learned a lot of things. There are three things which stick in my mind particularly. The first is the fact, mentioned in the talk of Bruno Kyewski, that antigens mimicking all tissues of the body are presented by medullary epithelial cells in the thymus. This allows future T cells to learn about all self antigens. I asked him afterwards if this includes tissues which are in the immunologically privileged sites, usually poorly accessible to the immune system, like the central nervous system. He confirmed that this is the case. The second is the fact, which came up in the talk of Marisa Torio, that T cell precursors in the thymus have the potential to develop into almost any type of white blood cell. This means that the fate of a cell to become a T cell is in general not decided before it reaches the thymus, the answer to a question I had often asked myself. The third is the description in the talk of Alfred Singer of the way in which it is decided which of the surface molecules CD4 or CD8 a T cell carries. I had already watched a video by Singer on this subject on the NIH web page but one thing I was not aware of was the fact that by binding the protein Lck it is possible for CD4 and CD8 to interfere with T cell signalling. Lck is sequestered and hence is not available for use by the T cell receptor.

Grossmann’s talk was mainly concerned with rather abstract ideas about cell signalling and it was hard for me to get to grips with them. I had the impression that the right mathematical context for these things should be control theory. The last and only really mathematical talk of the day, by Rob de Boer, was a highlight for me and not only for me. At dinner the air was buzzing with conversations on the subject. The talk was on monitoring the dynamics of immune cells by labelling with deuterium and drawing conclusions about their lifetimes. I had heard a talk on a similar subject by de Boer before at a conference in Dresden and I wrote about it briefly in a previous post. I liked that earlier talk but I liked the talk today much more. This was probably less due to the difference in content as to the fact that for whatever reason I now appreciated the significance of this work much better. This is an example where a mathematical model can be used to obtain information about processes in immunology which it is difficult or impossible to obtain in any other way. It is not that the mathematics is complicated, just some explicitly solvable linear ODE. The impressive thing is the direct contact this work makes with real biological questions like ‘how long does a memory T cell live’. Analysing different experiments both using deuterium in human subjects and other more poisonous substances which can only be used in mice originally gave inconsistent answers for lifetimes. With hindsight this arose from the assumption in the models of just one population of cells with a definite death rate. Passing to a model with two classes of cells largely removed the discrepancy. There was another interesting aspect of this lecture and its reception which explains its prevalence at dinner. It has to do with communication between different fields, in this case mathematics and biology. There was a lot of confusion among the audience which was due not to the factual content of the work but to the way the results were described and to the choice of language in describing the results. I should remember for the future that it is not enough to get an interesting result in mathematical biology. It is also necessary to be very careful about formulating it in the right way so as to make its meaning transparent for biologists.

The NFAT signalling pathway

January 6, 2012

The role of T cells in the immune system is to recognize foreign substances and then take appropriate action. In order for this to happen information must be propagated from the surface of the cell, where the T cell receptor is, to the nucleus in order to initiate DNA transcription. The last step in this process is the binding of a suitable combination of transcription factors to the DNA. NFAT (nuclear factor of activated T cells) is one of these transcription factors. The fact that the associated signalling pathway plays an important role in the activation of T cells explains the name. In fact this substance (or class of substances – there are actually five different ones) are important for signalling in many cells of the immune system. I already mentioned the NFAT signalling pathway, its connection to calcium and a paper on the subject by Salazar and Höfer in a previous post. Now I have written a paper where I look into mathematical aspects of the activation of NFAT by means of dephosphorylation and the role of calcium in this process. Salazar and Höfer introduced a high-dimensional dynamical system and computed stationary solutions in a slightly simplified version of that system. I now proved, using chemical reaction network theory, that for each choice of the many parameters in the system there exists exactly one stationary solution of the full system for each value of the total amount of NFAT in the cell. Every solution with that total amount of NFAT converges to the stationary solution at late times. Furthermore, this solution is well approximated by the explicit solution of the simplified system under a biologically motivated assumption that certain parameters are small enough. The main tool in the proof is the Deficiency Zero Theorem.

The result just mentioned concerns the model for the dephosphorylation process with the stimulation of the cell expressed through fixed choices of the parameters. In reality the stimulation is communicated through the calcium concentration in the cytosol. This means that the parameters in the model for desphosphorylation should be replaced by time-dependent functions which themselves are the result of a dynamical process. The situation is described by Salazar and Höfer with the help of a two-dimensional dynamical system closely related to one introduced by Somogyi and Stucki to describe calcium oscillations in liver cells. In the paper I did some analysis of the model, giving criteria for the stability of the unique stationary solution for given parameter values and the existence of periodic solutions. Hopf bifurcations play a role. The model is closely related to the Brusselator and techniques of proof can be imported from that case. In particular it is important to identify explicit invariant regions for the flow. When a solution of the model for the calcium concentration is such that it tends to a constant at late times then it can be shown that the resulting configuration of the phosphorylation states of NFAT also converges to the situation with constant coefficients previously analysed. When a solution converges to a periodic solution at late times it is not clear what can be said.


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