Watching T cells cross the blood-brain barrier

A recent press release by the Max Planck Institute for Neurobiology in Martinsried reports on a paper (‘Effector T cell interactions with meningeal vascular structures in nascent autoimmune CNS lesions’, Nature 462, 94) where detailed information is given on certain aspects of the way that activated T cells cross the blood-brain barrier during the development of the disease EAE in rats. In fact the authors were able to film the behaviour of the cells in living rats over extended time periods. In the best-known type of interaction between white blood cells and blood vessels through which they pass, the cells roll along the wall of the vessels until at some point they stop and exit the vessel by squeezing between the cells forming the wall. In this work the disease is provoked by introducing activated T cells which recognize myelin basic protein. In the case of most blood vessels they roll as just described but in the case of certain blood vessels belonging the BBB they instead crawl along the walls, often against the direction of the blood flow. This type of behaviour has apparently not been seen before in T cells although it is known from some other types of leukocytes. It looks as if the cells are searching for something particular although it is not clear what. Some of them eventually cross the BBB into the central nervous system while others let go and return to the bloodstream.

Once the cells get into the CNS they encounter phagocytic cells which activate them and cause them to produce substances such as interferon and interleukin 17. This then causes further T cells to be recruited to the CNS, thus leading to the full development of the disease. The identity of these phagocytic cells seems a bit mysterious. They are described in the paper as being intermediate between macrophages and dendritic cells. They are said to be constantly probing the region just outside the vessel walls. What I find particularly interesting about this work is that instead of just obtaining indirect information on what is going on it shows very directly what the cells are doing. The information presented in the paper is much more extensive that what I have just indicated. It has been possible to follow the cells on their way to deeper levels of the brain and to compare these particular T cells to other activated T cells which recognize a different antigen having nothing to do with CNS tissue.

Influenza vaccines

I have recently been reading about influenza vaccines and I am summarizing some of the information I found here. I start with some remarks on the classification of influenza viruses. The first distinction is between influenza A and influenza B viruses. The former are classified further into subtypes HnNm for numbers and . Well-known examples are H5N1 (which includes the recent ‘bird flu’) and H1N1 (which includes the pandemic of 1918 and the current ’swine flu’.) Influenza B does not carry a pandemic threat and will not be considered further here. Every year a vaccine is produced for the seasonal flu epidemic (in fact two – one for the southern and one for the northern hemisphere). It is trivalent, being directed against three types of virus. In recent years this has always been of the form H3N2 + H1N1 + B. In particular this is the case for the present vaccine for seasonal flu. It is not expected that this vaccine will be effective against the pandemic H1N1 swine flu. Thus a separate type of vaccine has been developed for that. In the classification H and N stand for haemagglutinin and neuraminidase, two proteins which occur on the surface of the virus and come in different forms in different strains. These are the main molecules of the virus recognized by antibodies. They are involved in the processes by which the virus enters and leaves host cells, respectively.

Next I come to some details concerning the vaccines themselves. I concentrate on those being applied in Germany since this is what would be relevant for me if I got vaccinated myself. I get the impression that there are a lot of unreliable and misleading statements on this subject in the media and so some care is necessary in judging the information available. On the web page of the Paul Ehrlich Institute there is a list of vaccines against seasonal flu approved in Germany in this season. Twenty products are listed. All are classified as inactivated. This means that if manufactured successfully the vaccine cannot lead to any reproduction of the virus. In other words the vaccine uses (parts of) ‘dead’ virus particles. Three of the vaccines are described as ‘virosomal’ which means that they can be administered as a nasal spray. Presumably all the others are administered by injection. Two of them include an adjuvant, a substance which is intended to amplify the immune response. This is one theme which has led to recent controversy in connection with swine flu vaccines and I will return to it later. One vaccine (Optaflu) is said to be produced in cell culture. This is connected to another theme of recent controversy, with discussion in the media about vaccines produced using cancer cells.

Having looked at the vaccines for seasonal flu I now come to swine flu vaccines.The web page of the Paul Ehrlich Institute lists three vaccines approved in Germany for the new H1N1 influenza. These are called Celvapan, Focetria and Pandemrix. All three are inactivated. The second and third include an adjuvant. The first is produced in cell culture. Apparently Pandemrix is intended to be the main vaccine used in Germany. There is a statement on the web page of the PEI that, contrary to some claims in the media, this is also what has been used to immunize the employees of that institute. There has been discussion of the fact that apparently politicians and the army are to get Celvapan so that a debate about ’second class citizens’ has taken place. This is likely to obscure the real issues. Consider next the topic of adjuvants, substances which have recently been getting some bad press. An adjuvant is a substance which increases the reaction of the immune system to an antigen given as a vaccine. A stronger immune response can lead to better immunity for a given amount of antigen. It could also in principle lead to an excessive and damaging immune reaction although I have not seen any convincing evidence that this has happened in the context of the swine flu vaccine. It would be wrong to think that the name adjuvant denotes a particular class of substances. Many different things can act as adjuvants. What they have in common is that they activate some part of the immune system. Given that the immune system is so interconnected this can lead to a stronger immune response on a wider basis. An interesting example is that in the combination vaccination for diphtheria, whooping cough and tetanus the diphtheria toxoid acts as an adjuvant for the other two vaccinations. What has just been said about the nature of adjuvants makes it clear that it is nonsensical to say that all adjuvants are bad. Each one must be considered on its own merits. In the case of Pandemrix the adjuvant is called AS03. I am unable to give any judgement on it, since I have not spent enough time studying the question. In any case my basic assumption is that what has been approved by the relevant medical authorities is OK. In other words, for these things my default attitude is trust, not mistrust.

Now to the question of the cancer cells. Celvapan is produced using a cell line called Vero cells which is derived from monkeys. It seems that these cells arose from kidneys of normal monkeys and have nothing to do with cancer. Usually normal cells can only undergo a limited number of divisions while cancer cells can be immortal. Vero cells are not cancer cells but they do seem to be able to survive in cell culture for an unlimited time. I do not understand how this works. It may be noted that Vero cells have been used in a routine way to produce millions of doses of polio vaccine and so there has been ample opportunity to discover any possible dangers associated to their use. In the production of Optaflu a cell line called Madin-Darby canine kidney cells is used. This looks like the same kind of tissue as with Vero cells, except derived from a different animal. I have not found a reference anywhere claiming the use of cancer cells in this context which looks trustworthy.

To finish, here is a piece of news from the web site of the ECDC in Stockholm. In the Ukraine there have now been 500 000 reported cases of acute respiratory illness and it seems that the expert opinion (cf. also the WHO website) is that most of these are related to the new H1N1 influenza. There have been 86 deaths reported from there. So it seems that the pandemic is alive and well.

Manipulating cells using light

In what follows I describe another subject which was a theme in the talk of Orion Weiner mentioned in the previous post. In the meantime I am familiar with the fact that there are techniques which allow us to see details of what is going on in cells. Here the most prominent protagonist is the green fluorescent protein (GFP) which was honoured by Nobel prizes in 2008. It allows information to be exported from the cell. This is a passive process in the sense that once the system has been prepared we just watch what happens. A more active process which is sometimes shown on video is that where a neutrophil follows the moving tip of a micropipette which is releasing a substance to which the cell is chemotactic. The subject of the present post is how it is possible to actively manipulate cells by sending in light of certain wavelengths. This may mean bathing the cell in light, illuminating certain precisely defined areas with a laser or a combination of the two.

The first type of experiment involves proteins which can be located either at the cell membrane or in the cytosol and which are fluorescently labelled so that their position can be monitored. It is possible to cause these molecules to move rapidly from the one localization to the other. This can be done on a time scale of a couple of seconds and it looks likes switching on and off a light. This can be done many times in a row. Here the effect on the cell is global. The second type of experiment has to do with localizing this type of effect. It allows patterns chosen by the experimenter to be projected onto the cell. Here coloured patches are visible. Their interpretation is that concentrations of a certain substance have been fixed according to the pattern. The third type of experiment is the most striking. Here a spot of light is moved over the cell and away from it in a certain direction. There results a long projection of the cell in that direction. On the video it looks as if the the cell is being pulled by a sticky object. All these things are done by switching on certain proteins which have been made light-sensitive.The sensitivity to light is achieved by incorporating elements which are responsible for allowing certain plants to react to light. One of the plants which acts as a source here is the favourite model organism among plants, Arabidopsis thaliana. The reference to the paper describing these results is ‘Spatiotemporal control of cell signalling using a light-switchable protein interaction’, Nature 461, 997-1001 (15 October, 2009).

Spiral waves in neutrophils

A few weeks ago I heard an interesting talk by Orion Weiner from the University of California at San Francisco. This contained a lot of information and it has taken me some time to get around to processing it. One of the things he talked about establishes a surprising link between two topics I have discussed before, chemotaxis and spiral waves. The idea is that the motion of the leading edge of cells such as neutrophils are driven by spiral waves in the concentrations of certain proteins. These waves have been filmed using sophisticated techniques of microscopy. The proteins involved belong to something called the WAVE complex. The name has nothing to do with waves. The WA in the name comes from ‘Wiskott-Aldrich syndrome protein (WASp)’. More specifically the protein whose concentration shows the wavelike phenomena is hematopoietic protein 1 (Hem-1). This protein interacts with the actin which is involved in the mechanics of the motion. However the waves are not visible in the concentration of the actin itself. More information about this and an interview with Weiner can be found here.

The cosmic no hair theorem

The last post was sparked off by a talk I heard at a conference in Oberwolfach. Here I will write about a topic where another talk at that conference looks like a big step forward. This was by Jared Speck. He was describing work of his with Igor Rodnianski which is not yet fully written up.

These days there is a wide consensus among astrophysicists that there is strong observational evidence to indicate that the expansion of the universe is accelerated. In other words it is not only the case that all distant galaxies are moving away from us (and from each other) but the velocity of recession is actually increasing. In the standard view this is only consistent with general relativity if there is a positive cosmological constant or some exotic matter called dark energy. For convenience I will not distinguish between these two in what follows. Dark energy leads to accelerated expansion and accelerated expansion causes spatial irregularities to be damped. The
geometry of spacetime and the matter distribution are smoothed. This kind of idea can be turned into a precise mathematical statement (maybe not uniquely) called the cosmic no hair theorem. From a mathematical point of view this is rather a conjecture than a theorem – at least it has been that way for most of the time it has existed. The name originates from a phrase of John Wheeler, ‘a black hole has no hair’. The idea of this was that a particular solution of the Einstein equations describing a black hole, the Kerr solution, should be attractor for the evolution of more general solutions containing a black hole. In other words a general class of solutions should evolve so as to look more and more like the Kerr solution. The Kerr solution depends only on two parameters. Thus in this scenario all the details get lost dynamically, leaving a very simple object with no complicated features, no hair. In models for an expanding universe with positive cosmological constant the smoothing process mentioned above also seems to drive all solutions towards an attractor, the de Sitter solution. It is this analogy which gave rise to the name ‘cosmic no hair theorem’.

The mathematical formalization of the cosmic no hair theorem says that a solution of the Einstein-matter equations with positive cosmological constant converges to the de Sitter solution at late times in a suitable sense. A weaker statement is that this should be true for solutions which start close to the de Sitter solution. The latter version can also be thought of as a kind of stability statement for de Sitter space. In the case of the vacuum Einstein equations the stability of de Sitter space was proved by Helmut Friedrich in 1986. Since our universe is certainly not empty the relevance of this result to cosmology is not immediately obvious. It turns out, however, that there are reasons to believe that the cosmological constant can often have a dominant effect on the late-time cosmological expansion which tends to make the effect of the matter into a higher-order correction. It is important to confirm these ideas by a theorem which includes the effect of matter. The most commonly used matter model in cosmology is a perfect fluid with linear equation of state. It contains a parameter which is often restricted by an inequality corresponding to perfect fluids which are less stiff than radiation. The result of Rodnianski and Speck is a form of the cosmic no hair theorem for precisely this class of matter models. The proofs build on previous work of Hans Ringström. Friedrich’s proof uses a technique (the conformal method) which is very powerful but rather rigid. It is difficult to see how to modify the proof to include matter such as a fluid, or indeed to replace the cosmological constant by some other kind of dark energy, such as a nonlinear scalar field. Ringström introduced more flexible methods which allowed him to obtain a version of the cosmic no hair theorem for dark energy modelled by certain types of nonlinear scalar field. His methods open up the perspective of including matter and this is what Rodnianski and Speck have now done. These methods use energy estimates, the workhorse of the theory of nonlinear hyperbolic equations, in a clever way. (I might say more clever than I am, since I once tried very hard to do this, without success.)

The result of Rodnianski and Speck is restricted to the case of irrotational fluids. I see no fundamental reason why this should be necessary. Nevertheless there is a clear technical reason – in the irrotational case the Euler equation of the fluid is equivalent to a nonlinear wave equation. On the level of formal power series the case with rotation works out, as shown in a paper of mine (Ann. H. Poincare 5, 1041). Another question is what happens for large data. In that case there are various restrictions.For sufficiently large data it is to be expected that black holes would be formed (even in the vacuum case). Moreover, the fluid can be expected to form shocks which means that the solution cannot be continued, at least in the realm of smooth solutions. I find it remarkable that the expansion caused by a positive cosmological constant is strong enough to suppress formation of shocks in a small data regime. There is just one result available on this subject for large initial data and inhomogeneous solutions. In this work, due to Blaise Tchapnda and myself (arising from Blaise’s PhD thesis, Class. Quantum Grav. 20, 3037) we treated plane-symmetric solutions of the Einstein-Vlasov system with positive cosmological constant. In this case the symmetry prevents formation of black holes and the choice of matter model allows any analogue of shocks to be avoided.

The Newtonian limit of general relativity

This week I am at a workshop on mathematical relativity at the Mathematical Research Institute in Oberwolfach which I am organizing together with Piotr Chrusciel and Jim Isenberg. I was a co-organizer of similar conferences here in 2000, 2003 and 2006. The institute organizes workshops fifty weeks in the year on all areas of mathematics and participation is generally by invitation only. The isolated setting of the institute in the Black Forest tends to create an intense research environment. Work is also stimulated by the fact that the institute has the best mathematics library in Germany which is no doubt also one of the best in the world.

There have been a lot of excellent talks here. One of these which was of particular interest to me personally was by Todd Oliynyk. His subject was connected with the Newtonian limit of general relativity. I mentioned this topic in a previous post as having been something whose importance was emphasized by Jürgen Ehlers. Unfortunately Jürgen did not live long enough to see some of his questions answered by the work which Oliynyk has been doing recently.

So what is the Newtonian limit? General relativity is, among other things, a theory of gravity which is fully relativistic. In standard textbooks on the subject we can read that Newtonian physics arises as a limit of general relativity when typical velocities in the system are small compared with the speed of light. Unfortunately it is quite unclear what this means mathematically. For instance, in general relativity gravity is described by the metric, a tensor with ten components, while in Newtonian gravity it is described by a scalar function. How can the former converge to the latter? The conceptual basis of the Newtonian limit was elucidated in work by many people over many years and these ideas were synthesized by Ehlers. On this basis I was able to prove a theorem about convergence to the Newtonian limit in 1994. This concerned asymptotically flat spacetimes (in physical terms isolated systems) and the matter was described by kinetic theory (Vlasov equation). I chose this type of matter since a more commonly used description, the perfect fluid, suffers from technical difficulties. This is because the equations degenerate when the fluid density becomes small and in an isolated system the density has to become small somewhere. The Vlasov equation is immune to these difficulties.

The key mathematical problems involved in the analysis of the Newtonian limit should be independent of the details of the matter model chosen. We just need some matter model which does not place obstacles in our way. In a way Oliynyk took this more literally than I did myself. I had proved an existence theorem for certain types of fluid bodies in general relativity by extending ideas introduced by Tetu Makino in the Newtonian case. These were far away from the generality which would be desirable from a physical point of view but they are good enough to play the role of matter sources when studying the Newtonian limit. This has been exploited by Oliynyk who used ‘Makino fluids’ as matter source in his results. The formulation of the Newtonian limit involves a family of solutions of he Einstein-matter equations depending on a parameter , roughly corresponding to where is the speed of light. The Newtonian limit is then the limit . What I proved in 1994 was the existence of families which are continuous in at . It is also interesting to know how smooth the family is at . The derivatives, when they exist, define higher order approximations to general relativity called the post-Newtonian approximations (PN for derivatives). I only got 0PN. Oliynyk has in the meantime reached 2PN. Results have been obtained for the asymptotically flat case which is the one most frequently considered in physics. It is well known that after 2PN the simple expansion breaks down. How can this be understood? My explanation (a little vague) is as follows. We are trying to approximate something which is bounded in its dependence on the spatial variables. Unfortunately above the 2PN level the approximation is not uniform and the coefficients in the expansion want to be unbounded. If you try to force them to be bounded by assumption the expansion breaks down. These coefficients are supposed to solve Poisson equations but the right hand sides have poor decay. The physicists typically try to represent the solutions of the Poisson equations in terms of the fundamental solution and get divergent integrals.

In his talk here Oliynyk reported that he has been able to treat post-Newtonian expansions of arbitrary order in the cosmological (spatially compact) case. It was a pleasant surprise for me that this works at all. When solving the Poisson equations in the cosmological case the right hand sides must have integral zero. It is remarkable that this works out at all. Once it is known that the procedure works at all, even for low orders, the intuition presented above makes it plausible that the obstructions familiar from the asymptotically flat case will not come up.

Returning to the asymptotically flat case, methods based on the post-Newtonian approximations are used to do the theoretical modelling for gravitational wave detectors whose cost is of the order of a billion dollars. It is an interesting comment on the role of mathematics in applications that nobody seems to worry too much about the almost entire lack of a rigorous mathematical foundation for these methods. In any case, the work I have been reporting on here represents the first steps on the road to changing this.

Formation of black holes in vacuum, part 2

I have just returned from a conference at the Mathematical Sciences Research Institute (MSRI) in Berkeley with the title ‘Hot topics: black holes in relativity‘. The central theme of this conference was the work of Demetrios Christodoulou on the formation of black holes in vacuum which I discussed in a previous post

On the first day of the conference I gave a talk on the characteristic initial value problem in general relativity. This was based on a paper I wrote more than twenty years ago (Proc. R. Soc. Lond. A427, 221 – I find it difficult to believe that it has been so long). The result of this paper is used in Christodoulou’s work and this was the main justification for the talk. In the ordinary initial value problem (Cauchy problem) for a hyperbolic system, or for the Einstein equations, initial data are prescribed on a spacelike hypersurface. The idea of the characteristic initial value problem is to instead prescribe data on a characteristic hypersurface. In fact it is necessary to use a singular characteristic hypersurface (such as a cone) or a pair of smooth hypersurfaces which intersect transversely. The result of Christodoulou is formulated in terms of the first of these possibilities, with data prescribed on a light cone. However he assumes that these data coincide with flat space data near the vertex of the cone, which allows the problem to be reduced to the second, easier possibility and it is the latter which I treated in my paper. In the result of that paper, which applies to smooth initial data, existence and uniqueness results for the characteristic initial value problem are deduced from the corresponding results for the Cauchy problem. In the ordinary Cauchy problem for the Einstein equations it is necessary to solve the constraint equations, which means solving an elliptic problem. In the characteristic case the constraints reduce to a hierarchical system of ordinary differential equations, which can be a big advantage.

During the conference Christodoulou gave five talks about his theorem and its proof and I found these very enlightening. I feel I have a much better understanding of the basics of this work now that I did before. One aspect of the result is that the data used are in one sense small (close to flat space data) and in another sense large. If they were small in a sufficiently strong sense then this should lead to a global existence result which in particular rules out the formation of black holes due to the theorem of Christodoulou and Klainerman on the stability of Minkowski space. On the other hand the interpretation of the result (formation of a trapped surface starting from a weak-field situation) requires that the data be small in some sense. Combining these two requirements (smallness and largeness in different senses) is a key feature of the theorem. It is also the case that the data are in some sense close to being spherically symmetric but in another sense far from spherical symmetry. Intuitively, it is necessary to have data which represent a sufficiently strong pulse of gravitational radiation. Spherical symmetry rules out gravitational radiation and this might be extrapolated to say that being close to spherical symmetry means restricting to a small amount of radiation.

In the proof of the theorem the solution is parametrized in the following way. The initial hypersurface is a null cone . It can be foliated by surfaces which are of constant affine distance from the vertex. Through each of these there is a null hypersurface transverse to which is taken to be a level hypersurface of a function . This function agrees with the affine distance (suitably normalized) on . A function is defined to be constant on the null cones of the points on a timelike curve passing through the vertex of the cone. Things are always set up so that these null hypersurfaces have no caustics. The two functions define a foliation by spheres by means of the intersections of their level hypersurfaces. This foliation is in a sense the analogue of that by symmetry orbits in a spherically symmetric problem. The fact that the problem is almost spherically symmetric is witnessed by the fact that the Gaussian curvature of these spheres is almost constant. Note that the gradients of the functions and do not commute as vector fields in general. Thus they are not tangent to surfaces and this is an important difference from spherical symmetry.

The initial data is such that a suitable energy density on the cone changes suddenly from being zero to being sufficiently large. This is the basis of the short pulse method, which is the central new technique in the proof of the theorem. What is this energy density? It is the norm squared of the trace-free part of the second fundamental form of the spheres in the direction along the cone.

When Christodoulou had completed his last lecture someone in the audience asked, ‘What’s next?’ In reply he announced that this had been his last project in general relativity, which came as quite a shock to the audience. The word ‘announced’ is perhaps not appropriate since it sounds too formal – he just said it spontaneously. This is sad news for the field of mathematical relativity but perhaps it is less sad in a wider context. After all, Christodoulou has a number of fascinating projects he is working on in other areas. At the same time the theorem I have been talking about here will probably be a beginning rather than an end. At the conference Igor Rodnianski gave a talk on work he has been doing with Sergiu Klainerman aimed at generalizing this result while understanding it more deeply. I look forward to seeing where that will lead.

The transcription factor T-bet

In the previous post I discussed tests for diseases. It is good to be able to get a high degree of certainty about whether an individual has a certain disease and this may have important implications for treatment. Under favourable circumstances a test may do more. Suppose that for a disease X there is a drug Y available which has the following properties. There is some, at least rough, quantitative measure for the severity of the disease at a given time. It is known that on average the severity of the disease is reduced by a significant percentage (e.g. 30%) when the drug is taken. It might, however, be that this average results from a few patients with a very large reduction in severity and a large number of patients with a small reduction in severity. Suppose that the drug is very expensive and has unpleasant side effects so that there is strong motivation not to prescribe it if it is not going to have a major benefit. Then it would be very useful to have a test which identifies those patients who are going to benefit before treatment is started.

A concrete example of the above is where the disease X is multiple sclerosis and the drug Y is one based on interferon . It has been suggested in a recent paper of Drulovic et. al. in the Journal of Neuroimmunology that the expression of a substance called T-bet in mononuclear cells in the blood may be prognostic for a good response to interferon treatment of MS patients. (A mononuclear cell means a white blood cell which is not a polymorphonuclear granulocyte.To say that T-bet is expressed in these cells means that they produce it.) Two other potential candidates for substances which might be prognostic, interferon and interleukin 17, do not give the same promising results.

So what is T-bet? The name, which was introduced in 2000, stands for ‘T-box expressed in T cells’. The name T-box denotes a class of genes which code for transcription factors. Note that the same name is often used for a gene and the protein it codes for. A transcription factor is a protein which binds to DNA and increases or decreases the extent to which certain genes are transcribed into RNA. It therefore influences the amount of the corresponding protein which the cell produces. Transcription factors are important for cell differentiation. All cells in the body have the same genes (almost – I do not want to get into exceptions here) and it is the expression of the genes in a given cell which determines which type of cell it is. As has been mentioned in previous posts T helper cells come in at least two types, Th1 and Th2, and a shift to a higher proportion of Th1 cells seems to be bad for MS. The substances T-bet and interferon are involved in the process of differentiation, pushing the cells towards Th1. In particular, T-bet seems to be the master regulator of this process. The details of the process are complicated. A recent paper by Edda Schulz, Luca Mariani, Andreas Radbruch and Thomas Höfer (Immunity 30, 673) has studied this both experimentally and theoretically.The theoretical part uses a mathematical (ODE) model. As mentioned in a previous post there is also another class of T cells called Th17. The difference between IL-17 and T-bet in MS indicated above seems to indicate that in that disease Th1 cells are more important than Th17 cells.

Rheumatoid factor

We are familiar with the fact that it is possible to do tests for various types of disease. A well-known example are tests for HIV, often called AIDS tests in everyday language. I asked myself the question to what extent there are also reliable tests for autoimmune diseases. If there is no pathogen such as a virus present then one approach to tests is ruled out. But are there others? One relevant example I found is that of rheumatoid arthritis (RA) and tests based on a substance called rheumatoid factor. I will say more about this below but first I wanted to recall one well-known pitfall of tests in general. This shows that the notion of a reliable test is not completely obvious. It is useful to introduce some terminology. The sensitivity of a test is the proportion of people having the disease for which the test gives a positive result. The specificity is the proportion of people not having the disease for which the test gives a negative result. Consider the example of a disease which affects one person in one million and a test where the probability of a positive result in someone who does not have the disease is one in ten thousand. In this case the specificity is 0.9999, which sounds very good. Suppose now, however, one million people are tested. The expected number of people in the sample having the disease is one but the number of people who will test positive is one hundred. In other words a positive test only really says that the probability of the patient having the disease is at least one per cent, a rather weak statement. The problem here is simply that looking for an effect which is very rare can make reliable testing very hard. The quantity which comes out to be one per cent in this example is called the positive predictive value.

After this digression I now come back to rheumatoid factor. Autoimmune diseases can be divided into those where the immune system attacks a particular tissue (e.g. insulin dependent diabetes mellitus where it is the cells of the pancreas which are attacked) and those which are systemic and affect a variety of tissues. RA is of the latter type although its best-known effects concern the joints. The presence of rheumatoid factor is an indication of RA but it may also be present in people suffering from Sjögren’s syndrome or in healthy individuals. Thus, in the above terminology, the specificity of the test is not very high. It also happens that rheumatoid factor is not detectable in people with RA during extended periods. To sum up, this is test for RA but it does not seem to be a very precise one. What kind of substance is rheumatoid factor? I mention at this point, since it is something that used to confuse me, that the words ‘antibody’ and ‘immunoglobulin’ are synonymous. Rheumatoid factor is an immunoglobulin of type M against immunoglobulins of type G. The antigen it binds to is in the Fc part of the antibody. This is a part which is independent of the antigen for which the antibody is specific and only depends on the isotype. The isotype differs between antibodies with different functional properties and is designated by the letter M, D, G, A or E. There is another test for RA with better specificity using anti-citrullinated protein antibodies. Citrulline is a non-classical amino acid. It is not coded for by DNA but can be produced by modification of existing proteins.

What about other autoimmune diseases? Another important systemic autoimmune disease is systemic lupus erythematosus (SLE). Here a common test involves antinuclear antibodies, i.e. antibodies against parts of the cell nucleus. The test has high sensitivity but low specificity. In the case of multiple sclerosis there seems to be no test comparable to those just mentioned. One diagnostic criterion which is used is that of oligoclonal bands. What this means is the occurrence of proteins in the cerebrospinal fluid (actually immunoglobulins of type G) which show up as bands in electrophoresis. It is important that there are a few of those bands (oligo) in the cerebrospinal fluid which are not present in the blood. This is regarded as evidence of activity of the immune system within the central nervous system. The difference to the tests discussed above is that little seems to be known about what substances the antibodies producing the bands are antibodies against.

How to be unhappy

There are many books on the market which give advice as to how to improve your life. I feel attracted to this kind of book, which of course shows something about how satisfied I am with my own life. I particularly like the classic ‘How to stop worrying and start living’ by Dale Carnegie which I have read several times. This is an old book, going back to 1944, but this does not matter. Circumstances change but human nature, which is at the centre of this type of book, does not. I like Carnegie’s down to earth approach. I also like the fact that he makes clear that the main things he has to say are not new – his purpose is to remind us of things which in principle we already know but which are all too often forgotten. I feel that I have really profited from reading that book.

The reason I am writing this post is that I just read a book called ‘Anleitung zum Unglücklichsein’ by Paul Watzlawick, which I came across in the public library. I found this book very amusing and entertaining. The title can be translated as ‘Guide to being unhappy’. I am not aware that it has been translated into English. The list of references includes a book called ‘How to make yourself miserable’ by Dan Greenburg, which may be similar.Returning to the book of Watzlawick, it is not likely to make its readers unhappy. It is full of biting humour. It is a kind of parody of the self-help books I mentioned above but in a sense it can have similar effects. It lays bare certain mechanisms in human thinking and in the communication between individuals. This is not a easy book to read. It is necessary to pay careful attention so as not to occasionally take what is written there literally. Reading the book is a rewarding experience. It underlines the fact that the meaning of the word ‘happiness’ (Glück) is not so obvious as is generally assumed.