## Archive for October, 2010

### Glycobiology

October 28, 2010

Yesterday I heard a talk by Peter Seeberger about his research group at the Max Planck Institute for Colloids and Interfaces. That institute is based in Golm but through this event I discovered that in reality Seeberger’s group is at present housed in buildings belonging to the Free University in Dahlem. They will only move once a new extension to the building in Golm is ready. Seeberger’s speciality is the synthesis of complex sugars from monosaccharides. After the talk there was a guided tour of the laboratories and we saw a machine for the synthesis of peptides. In that group it is actually being used to make other types of polymers. If it was being used for peptide synthesis it would just be possible to type in the sequence of the desired peptide and press a button. (Maybe I am oversimplifying here but we were told that almost anyone could use the machine, without any special knowledge of chemistry.) Seeberger’s speciality is an analogous machine for the much more difficult task of making polysaccharides with any desired structure.

This has important applications to biology. For instance, cells are decorated with various glycoproteins, glycolipids and other compounds containing sugars on their surfaces. They are important for the recognition of cells and for the entry of pathogens. As a consequence it is easy to see that antibodies against sugars should be important for biology and medicine. In the talk it was mentioned that certian harmful effects of the malaria pathogen are due to a toxin that it produces and that this toxin is a polysaccharide. In endemic areas many people, in particular children, are apparently healthy despite high loads of the parasite in their blood. The explanation for this is that they have antibodies against the toxin. Neutralizing the toxin removes the most serious (and possibly fatal) effects of the pathogen although the organism remains plentiful. It was explained that the immune system of small children cannot recognize sugars so that they may die before they can develop this protection. A possible treatment is to give them a kind of vaccine to raise these antibodies. A substance developed by Seeberger is at an advanced stage of preclinical testing. He also said that vaccines based on polysaccharides are less likely to be met by resistance than more conventional ones based on peptides since the process of producing sugars in cells is so much more indirect than the that of transcription and translation leading from DNA to protein.

### More on the inflammasome

October 21, 2010

In a previous post I mentioned the inflammasome. Today I heard a talk about this by Jürg Tschopp from Lausanne who is the father of this subject in the sense that the concept and the name were invented in his lab in 2002. I learned that there are many different inflammasomes, i.e. many different protein complexes of this type. The one he concentrated on most in his talk involves a protein called NALP3. The inflammasome is involved with the occurrence or maintenance of inflammation. This may occur as a reaction to PAMPs (pathogen-associated molecular patterns) or DAMPs (danger-associated molecular patterns). The former are sensed by toll-like receptors while the others, less-well known, are associated with NOD-like receptors. He presented a very long list of diseases and other substances causing inflammation which are known or suspected to activate an inflammasome. The substances independent of pathogens mentioned included uric acid crystals, asbestos, alum (which is a constituent of some adjuvants) and nanoparticles. The typical outputs of the inflammasome are IL1$\beta$ and IL18. There is a disease (or rather a group of related diseases) called CAPS (cryopyrin-associated periodic syndromes) where the inflammasome is defective and this presents an opportunity to learn about its functions.

He went on to talk about three diseases where the inflammasome may play an important role: gout, type II diabetes and MS. Gout is a disease where crystals of uric acid accumulate in the joints, causing deformity (he had some pretty horrifying pictures) and intense pain. Gout patients have attacks which can be treated with medication e.g. corticosteroids. Several days of treatment are necessary and the improvement does not last very long. He reported on successes in treating gout with anti-IL1$\beta$. In that case the treatment is effective after one day and can last for a year. This means that the positive effects of one injection lasts a year! He reported similar results on anti-IL1$\beta$ as a treatment for type II diabetes. The prospect he was presenting was that one injection of this substance could replace the innumerable insulin injections of a diabetes patient in a whole year. This treatment is the subject of phase 2 clinical trials by Novartis. It could even be the case that the $\beta$-cells, which have been partially destroyed in this disease, start to regenerate.

In the case of MS Tschopp was linking the inflammasome with IFN$\beta$ therapy. Apparently this substance inhibits activation of the inflammasome. He mentioned experimantal data which show that MS patients being treated with IFN$\beta$ exhibit reduced inflammasome activity in response to certain antigen challenges in comparison to healthy controls. I must say that some of the things I heard in this lecture sounded almost too good to be true. The speaker himself said that he has found the success of some of the clinical trials very surprising. Maybe this is really the beginning of a major new development in medicine. Could anti-IL1$\beta$ overtake anti-TNF$\alpha$ some day?

### Chemical reaction network theory

October 6, 2010

Models of biological phenomena often include complicated networks of chemical reactions. I have made some comments on this in a previous post. From a mathematical point of view this leads to large systems of ordinary differential equations (or possibly reaction diffusion equations) depending on a large number of parameters, whose precise values are often not known. At first sight it seems hopelessly complicated to prove general theorems about the dynamics of solutions of these systems. Surprisingly something can be done and it is interesting to enquire why. These ideas are associated with the name ‘chemical reaction network theory’. What are the special features of these systems which allow something to be done? The first property is that they are sparse. This means that the right hand side of the evolution equation for a given quantity only depends on a few of the other unknowns. The second is that with the choice of mass action or Michaelis-Menten kinetics, which are the simplest and most common ways of modelling the reactions, the problem of finding stationary solutions reduces to finding real solutions of systems of polynomial equations. This opens up the possibility of applying tools from (real) algebraic geometry. It is also the case that there is quite a lot of linear structure in the coefficients which allows the application of sophisticated techniques of linear algebra. In practise the first question which people would like to answer is whether there are biologically reasonable stationary solutions and if so how many. In particular, is there more than one (multistability)? The dynamics of these systems do often turn out to be relatively simple. It is also often the case that the qualitative behaviour depends only weakly (if at all) on the choice of parameters. I do not know to what extent this is a selection effect, i.e. that the examples which get into the literature are preferentially those which have these simple properties.

This theory started with a 1972 paper by the chemical engineers Fritz Horn and Roy Jackson (Arch. Rat. Mech. Anal. 47, 81). It seems that in later years the one who contributed most to the development of the subject was Martin Feinberg. For these systems it is possible to introduce a non-negative integer called the deficiency $\delta$ and the case where $\delta$ is zero is the simplest one. The fact that something can be said about the dynamics of solutions in this case which goes beyond statements about the existence of stationary solutions is due to the existence of a Lyapunov function. The source of this function is explained in the paper of Horn and Jackson. In certain cases it is closely related to the Helmholtz free energy which is required to decrease by thermodynamic arguments. The deficiency zero theorem says that the dynamical behaviour is determined by a property called weak reversibility. To explain this property I need some basic concepts. The unknowns in the dynamical system corresponding to a chemical reaction network are the concentrations of the chemical species involved, i.e. the different chemical substances. A complex is a formal linear combination of species with positive integer coefficients. Each reaction in the network corresponds to an ordered pair of complexes, which are the left hand side and right hand side of the reaction. A network is called weakly reversible if whenever there is a concatenation of reactions leading from a complex $y$ to a complex $y'$ there is also one from $y'$ to $y$. When $\delta=0$ if a network is not weakly reversible then the corresponding dynamical system with mass action kinetics has no stationary solutions where all concentrations are positive. It also has no periodic solutions. If it is weakly reversible there is exactly one such stationary solution which is a global attractor for the system. More precisely, there are invariant manifolds called stoichiometric compatibility classes and the statements about uniqueness and stability refer to a given class of this type. Note that, in particular, a deficiency zero system can never have more than one relevant stationary solution (within a stoichiometric compatibility class).

There is a generalization of the deficiency zero theorem called the deficiency one theorem. To explain this it is necessary to introduce the notion of linkage classes. Given a network a graph can be defined whose nodes are complexes and where there there are edges joining these nodes corresponding to reactions. The connected components of the resulting graph are the linkage classes. Each component defines a network of its own and so has a natural definition of deficiency. It can be shown that the sum of the deficiencies of the linkage classes is no greater that the deficiency of the whole network. I will not describe all the hypotheses of the deficiency one theorem here. I will just mention that they include the conditions that no linkage class has a deficiency greater than one and that the sum of the deficiencies of the linkage classes is equal to the deficiency of the whole network.