# Hydrobates

A mathematician thinks aloud

## Conference on modelling the immune system in Dresden, part 3

In my second ever post on this blog I quoted a celebrated paper of Ho et. al. on HIV therapy. One of the other authors of that paper was Avidan Neumann and on Wednesday I had the opportunity to hear him giving a talk. His subjects were HIV, HBV and HCV, with the greatest emphasis on the last of these. He did briefly mention the case of the man who is apparently the only person ever to be cured of HIV. This took place in Berlin in 2006. The man had both HIV and leukemia and as therapies for both of these he was given radiation treatment and a bone marrow transplant. The transplant was a very special one since the donor was an HIV controller. Since then the patient has not had any treatment against HIV and despite very thorough tests it has been impossible to find any trace of HIV in his body.

Coming now to HCV, this virus causes hepatitis C, a liver disease which is often chronic. It often has few or no symptoms but the liver is progressively damaged, frequently resulting in cirrhosis or even liver cancer. In the worst case a liver transplant is required and after the transplant the virus always infects the new liver. This disease affects about 300 million people and no vaccine is available. The standard treatment is to give interferon $\alpha$ and an antiviral drug ribavirin over many months and this can be very hard on patients due to side effects. A new treatment, a protease called telaprevir, may soon be approved by the FDA. It is much more effective in getting rid of the virus than the standard treatment. The reasons why it is effective have been understood using mathematical modelling. Listening to this talk gave me the impression how close medicine and mathematics can be.

Arup Chakraborty gave a talk on targets for HIV vaccines which had an essential connection to HIV controllers. He has done statistical analysis of HIV viral genomes looking for a certain type of pattern. He explained the idea by an analogy with the fluctuations of share prices. If the share prices of different companies are examined for positive correlations then it is discovered that they can be grouped into certain sectors. These are the companies which are strongly related to certain activities, for instance those which have some close connection to car production. The genome of HIV virions can be analysed for correlations in an analogous way. This results in the identification of positively correlated groups which may again be called sectors. It is not a priori clear what these groups really mean. Interestingly the group with the strongest correlations (Sector 3 if I remember correctly) contains sequences related to HIV controllers. It turns out that these sequences have to do with the activity of building the viral capsid. A problem with vaccines against HIV is that if a vaccine targets a particular peptide a mutation may change that peptide and destroy the recognition without damaging the virus too much. Thus the virus can escape the immune attack. The special sequences in Sector 3 are such that mutations which affect them are likely to affect the stability of the capsid and hence compromise the reproduction of the virus. An important role is also played by those MHC molecules which can present the special peptides. The MHC molecules which do this optimally, and which occur in controllers are rare in the general population. They are, however, presented in a subleading way by more common MHC molecules. This may be enough to form an element of designing a good vaccine. In analysing this problem Chakraborty is using sophisticated mathematics, in particular the theory of random matrices.

To sum up my impressions of the conference, it has convinced me that mathematical immunology is an exciting and dynamic field which I want to be a part of.
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