## Archive for September, 2010

### Ernst Schering prize lecture by Feldmann and Maini

September 29, 2010

Yesterday Sir Marc Feldmann and Sir Ravinder Maini from Imperial College were awarded the Ernst Schering prize in recognition of their development of the monoclonal antibody infliximab as a therapy for rheumatoid arthritis. In fact, as far as I know, this was the first therapy of this type to be used for any autoimmune disease. Today they gave a corresponding lecture at the Charite in Berlin and I was fortunate enough to be able to attend. A remarkable aspect of their achievement is that they were intimately involved in the whole process from a theory of Feldmann concerning the mechanism of autoimmune diseases to seeing the drug through clinical testing. One point which was mentioned several times by them and others was that this kind of development would probably be impossible today due to EU regulations. They showed a film clip in black and white of one of the first patients they treated with the new method, a young woman. First she was shown before the therapy coming down stairs with great difficulty, clinging to the banister. Then whe was shown a few weeks later, after the therapy, running, or almost skipping, down the same stairs, a picture of health. It was pointed out that she was not a typical patient since she was young and she had only had RA for a relatively short time before therapy. Interestingly, the initial trials of this drug were done on a ‘single-blind’ basis. The use of this type of drug was so new that it was considered too risky for the doctors doing the treatment not to know who was getting treated so that their state could be monitored closely. I noted on one transparency that it was written that the patients were treated sequentially. This made me think involuntarily of the recent disaster with the trials of one drug where care was not taken to start giving the drug to different patients after a long enough time interval. Infliximab and other antibodies against tumour necrosis factor $\alpha$, alone or in combination with methotrexate have revolutionized the treatment of RA. The disease cannot be cured, but its progression can be stopped. A picture was shown of one older woman, evidently moving forward with great difficulty with a walking frame and with her body very deformed by the disease. The comment from one of the speakers was that this is something which is no longer seen in clinics. The importance of these drugs can be seen by the fact that 15 billion per year is spent on them.

The lecture also generated some mathematical thoughts in me. In the early days of these developments knowledge was available about various cytokines in the joints of patients with RA. Feldmann described the special role of TNF$\alpha$ as being the rate-limiting step. This conjured up for me a picture of a dynamical system describing the concentrations of various cytokines, with one of the variables describing TNF$\alpha$. What is its special role in comparison with, for instance, IL1 which had previously been believed to be of central significance? The data say that administering antibodies to TNF$\alpha$ leads to a fall in the concentration of IL1 and various other cytokines, both inflammatory and anti-inflammatory. On the other hand, administering an antibody to IL1 does not lead to a significant decrease in the concentration of TNF$\alpha$. How can we think of this in terms of the dynamical system? An antibody can function as a knockout – it effectively sets the coefficient in front of the terms describing the production of the corresponding antigen to zero. Then the hyperplane where its concentration vanishes becomes invariant and carries a new dynamical system. The original system has a stationary solution where all concentrations are positive. The knockout system has a similar stationary solution and the question is how the concentration of a given substance compares in the two cases. Later on in the talk there was discussion of finding other substances upstream of TNF$\alpha$ as a basis for new therapies. What does that mean? Intuitively if $X$ is upstream of $Y$ it means that the production of $X$ causes the production of $Y$. A symptom of this could be that a knockout of $X$ leads to a decrease of $Y$. Thus what is special about TNF$\alpha$ is that it is far upstream.

I was very impressed by the achievements of the two speakers and by the account they gave of their work. It was also clear that they are very active in pushing these ideas further. Might they get a Nobel prize sometime soon? I for one would not be sorry if they did.

### Legionella and molecular mimicry

September 23, 2010

Today I heard a talk by Carmen Buchrieser from the Institut Pasteur about Legionella, the bacterium which causes Legionnaire’s disease. This disease was first observed in 1976. At a meeting of US military veterans in a hotel in Philadelphia many fell ill with an unknown respiratory disease and an alarming number of those affected died as a consequence. The bacterium was discovered early in the next year and given the name Legionella pneumophila. Infection with this disease can be fatal but is usually only so in older people or those who are immunocompromized. The disease is not passed directly between humans. In the words of the speaker, the human lung is a dead end for Legionella. A bacterium of this kind which enters one human host will never leave. The sources of infection in humans are water droplets from cooling towers,air conditioning systems, showers etc.

The natural hosts of Legionella are amoebae. In humans they infect pulmonary macrophages which could be thought of as surrogate amoebae in this context. Because of the lifestyle of the species there is no evolutionary pressure on it resulting from its time spent in humans. The pressure comes from its natural life in the amoeba. I have mentioned molecular mimicry in a previous post as a phenomenon relevant to immunology. In this post I am using it to mean something more primitive, namely a similarity in the genes of hosts and their parasites. When the host is a vertebrate this has an implication for immunity but in the case of Legionella the principal host is the amoeba, so that this is not relevant. This bacterium does have a wide variety of proteins which resemble proteins of eukaryotes. The speaker mentioned two ways in which molecular mimicry could have arisen in Legionella. One is horizontal gene transfer, i. e, the transfer of genes between different species. The other is convergent evolution. I did not have the impression that it is clear which if these two is more important.

### Leishmaniasis

September 17, 2010

Yesterday I heard a talk by Ingrid Müller from Imperial College about leishmaniasis, a disease caused by protozoa of the genus Leishmania. The genus is named after the Scottish pathologist and army medical officer William Leishman. The life cycle of the parasite is of a similar type to that of the organism which causes malaria. Humans are infected by the bite of a sand fly (instead of mosquito in the case of malaria) and the individual infected in this way then passes on the parasite to other sand flies taking blood meals. While the malaria parasite makes its way to red blood cells the preferred target of Leishmania are macrophages, where it lives in certain vesicles. In this sense it is similar to the tuberculosis bacterium and has to meet similar challenges, such as not being digested. There are different forms of leishmaniasis. The cutaneous form, which is the most common, affects the skin and is cleared by the immune system after some time. Another, the visceral form, is much more serious. In the latter case the parasite damages internal organs and may be fatal if not treated. It could be said that cutaneous leishmaniasis is not a very serious disease, compared to many others. Unfortunately even when the lesion on the skin heals it can leave the affected person seriously disfigured. Thus there is a strong motivation for combatting it. Not surprisingly leishmaniasis is only common in parts of the world where poverty is widespread (Africa, South America, India) although cases do also occur in southern Europe. In parts of India the visceral form is known under the name kala azar. Searching for this disease on the internet you find a relatively large number of sites relating to dogs. What is behind this is the following. Dogs can also be affected by these parasites. When dog-lovers bring stray dogs from Spain to Germany (for instance) there exists an appreciable risk that the dogs may bring the parasites with them. Thus care is necessary.

Leishmaniasis is much less well-known than malaria and the available scientific knowledge of the disease and (as a natural consequence) the available treatments are much more rudimentary. What treatments there are are expensive, which is particularly problematic in the regions where they are necessary. Leishmaniasis is also much less common than malaria but in fact no up to date and reliable epidemiological data is available so that it is not clear how common it is. Infections of mice with Leishmania have been a popular model system in immunology. The cutaneous and visceral forms have been associated with Th1 and Th2 type responses respectively in the past. According to the speaker this association is controversial. A simple picture would be that a Th1 response results in a high concentration of interferon $\gamma$ which activates macrophages and thus allows them the kill the parasites infecting them. It was mentioned in the talk that macrophages can also be activated in a different way by IL4 (the typical Th2 cytokine) in what is called alternative activation. This leads to production of the enzyme arginase which metabolises arginine. In the talk evidence was presented that the resulting metabolites can serve as raw materials for the replication of the parasite in the hostile environment of the phagosome. This has been supported by showing that parasite growth can be accelerated by adding metabolites downstream of arginine, such as ornithine. What I heard in this talk has contributed to my opinion that while the Th1-Th2 axis is useful for generating ideas for understanding various diseases it is necessary to keep in mind that it is likely to be an oversimplification of a complex state of affairs.

### Self-similar solutions of the Einstein-Vlasov system

September 15, 2010

The Einstein-Vlasov system describes the evolution of a collisionless gas in general relativity. The unknown in the Vlasov equation is a function $f(t,x,v)$, the number density of particles with position $x$ and velocity $v$ at time $t$. A regular solution is one for which the function $f$ is smooth (or at least $C^1$). These equations can be used to model gravitational collapse in general relativity, i.e. the process by which a concentration of matter contracts due to its own weight. I concentrate here on the case that the configuration is spherically symmetric since it is already difficult enough to analyse. It has been known for a long time that a solution of this system corresponding to a sufficiently small concentration of matter does not collapse. The matter spreads out at late times, with the matter density and the gravitational field tending to zero. More recently it has been proved that there is a class of data for which a black hole is formed. In particular singularities occur in these equations. It is of interest to know whether singularities can occur which are not contained in black holes. This is the question of cosmic censorship.

One way of trying to prove cosmic censorship involves investigating whether general initial data give rise to solutions which are global in a certain type of coordinate system. In spherical symmetry this has been looked at for the Schwarzschild coordinates. Here we can ask whether solutions are always global in Schwarzschild time. This statement is consistent with the presence of a black hole since in that case it can happen that the coordinate system being considered only covers a region outside the black hole. For general smooth spherically symmetric initial data this global existence question is open. A number of people, including myself, have put a lot of time and effort into proving global existence for this problem but this enterprise has not yet been successful. In view of the fact that research on this subject seems to be stuck it makes sense to think about trying to prove the opposite statement, in other words to prove that there are data for which global existence fails. This might in principle lead to either a positive or a negative answer to the global existence problem. An investigation of this type is being carried out by Juan Velázquez and myself and we have just written a paper on this. I will now explain what we were able to prove.

A type of matter which is frequently studied in general reletivity is dust, a perfect fluid with zero pressure. It has unpleasant mathematical properties and a strong tendency to form singularities even in the absence of gravity. Solutions of the Einstein-dust system can be interpreted as solutions of the Einstein-Vlasov system which instead of being regular have a Dirac $\delta$ dependence on the velocity variables. For fixed $(t,x)$ the support of $f$ in $v$ is a single point. In a smooth solution this support is three-dimensional. In the paper we look at a class of solutions where the support is two-dimensional. These solutions are self-similar. The construction of solutions of the type considerd in the paper can be reduced to the study of certain solutions of a four-dimensional dynamical system depending on two parameters. There is a point $P_0$ is the phase space defined by the application and a stationary solution $P_1$ depending on the parameters. What needs to be shown is that for suitable values of the parameters the solution which starts at $P_0$ converges to $P_1$ for large values of the independent variable. In more detail, when one of the parameters $y_0$ is fixed to be positive and sufficiently small there exists a value of the other paramater $\theta$ for which this statement holds. The proof is a shooting argument. This uses a family of initial data for a three-dimensional dynamical system depending on a parameter $q_0$. (The relation of the three-dimensional system to the original four-dimensional one is too complicated to be described here.) It is proved that the solution has one type of asymptotic behaviour for small values of $q_0$ and another for large values of $q_0$. It is shown that there must be at least one intermediate value of the parameter for which the asymptotics is of the type required to construct the solution of interest of the Einstein-Vlasov system. Shooting arguments are rather common when constructing solutions of ODE numerically. Here we have an example where similar ideas can be used to obtain an existence proof.