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.
Hydrobates 
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