## Archive for September, 2016

### In the beginning was the worm

September 29, 2016

In a previous post I mentioned the book by Andrew Brown whose title I have used here. I came across it in a second hand bookshop in Berkeley when I was spending time at MSRI in 2009. I read it with pleasure then and now I have read it again. It contains the story of how the worm Caenorhabditis elegans became an important model organism. This came about because Sydney Brenner deliberately searched for an organism with favourable properties and promoted it very effectively once he had found it. It is transparent so that it is possible to see what is going on inside it and it is easy to keep in the lab and reproduces fast enough in order to allow genetic research to be done rapidly. The organism sought was supposed to have a suitable sexual system. C. elegans is normally hermaphrodite but does also have males and so it is acceptable from that point of view. One further important fact about C. elegans is that it has a nervous system, albeit a relatively simple one. (More precisely, it has two nervous systems but I have not looked into the details of that issue.) Brenner was looking to understand how genetics determines behaviour and C. elegans gave him an opportunity to make an attack on this problem in two steps. First understand how to get from genes to neurons and then understand how to get from neurons to behaviour. C. elegans has a total of 302 neurons. It has 959 cells in total, not including eggs and sperm. Among the remarkable things known about the worm are the complete developmental history of each of its cells and the wiring diagram of its neurons. There are about 6400 synapses but the exact number, unlike the number of cells or neurons, is dependent on the individual. For orientation note that C. elegans is a eukaryotic organism (in contrast to phages or E. coli) which is multicellular (in contrast to Saccharomyces cerevisiae) and it is an animal (in contrast to Arabidopsis thaliana). Otherwise, among the class of model organisms, it is as simple and fast reproducing as possible. In particular it is simpler than Drosophila, which was traditionally the favourite multicellular model organism of the geneticists.

In this blog I have previously mentioned Sydney Brenner and expressed my admiration for him. I have twice met him personally when he was giving talks in Berlin and I have also watched a number of videos of him which are available on the web and read various texts he has written. In this way I have experienced a little of the magnetism which allowed him to inspire gifted and risk-taking young scientists to work on the worm. Brenner spent 20 years at the Laboratory of Molecular Biology in Cambridge, a large part of it as director of that organization. In the pioneering days of molecular biology the lab was producing Nobel prizes in series. He had to wait until 2002 for his own Nobel prize (for physiology or medicine), shared with John Sulston and Robert Horvitz. In his Nobel speech Brenner said that he felt there was a fourth prizewinner, C. elegans, which, however, did not get a share of the money. My other favourite quote from that speech is his description of the (then) present state of molecular biology, ‘drowning in a sea of data, starving for knowledge’. Since then that problem has only got worse.

Now I will collect some ‘firsts’ associated with C. elegans. It was the first multicellular organism to have its whole genome sequenced, in 1998. This can also be seen as the point of departure for the human genome project. Here the worm people overtook the drosophilists and the Drosophila genome was only finished in 2000. Sulston played a central role in the public project to sequence the human genome and the struggle with the commercial project of Craig Venter. It was only the link between the worm genome project and the human one which allowed enough money to be raised to finish the worm sequence. According to the book Sulston was more interested in the worm project since he wanted to properly finish what he had started. Martin Chalfie, coming from the worm community introduced GFP (green fluorescent protein) into molecular biology. He first expressed it in E. coli and C. elegans. He got a Nobel prize for that in 2008. microRNA (miRNA) was first found in C. elegans. It is the basis of RNA interference (RNAi), also first found in C. elegans. This earned a Nobel prize in 2006. The genetics of the process of apoptosis (programmed cell death) was understood by studying C. elegans. When Sulston was investigated the cell lineage he saw that certain cells had to die as part of the developmental process. Exactly 131 cells die during this process.

To conclude I mention a couple of features of C. elegans going beyond the time covered by the book. I asked myself what we can learn about the immune system from C. elegans. Presumably every living organism needs an immune system to survive in a hostile environment. The adaptive immune system in the form known in humans only exists in vertebrates and hence, in particular, not in the worm. Some related comments can be found here. It seems that C. elegans has no adaptive immune system at all but it does have innate immunity. It has cells called coelomocytes which have at least some resemblance to immune cells. It has six of them in total. Compare this with more than $10^9$ immune cells per litre in our blood. C. elegans eats bacteria. These days the human gut flora is a fashionable topic. A couple of weeks ago I heard a talk by Giulia Enders, the author of the book ‘Darm mit Charme’ which sold a million copies in 2014. I had bought and read the book and found it interesting although I was not really enthusiastic about it. Now TV advertising includes products aimed at the gut flora of cats. So what about C. elegans? Does it have an interesting gut flora? The answer seems to be yes. See for instance the 2013 article ‘Worms need microbes too’ in EMBO Mol. Med. 5, 1300.

### Models for photosynthesis, part 4

September 19, 2016

In previous posts in this series I introduced some models for the Calvin cycle of photosynthesis and mentioned some open questions concerning them. I have now written a paper where on the one hand I survey a number of mathematical models for the Calvin cycle and the relations between them and on the other hand I am able to provide answers to some of the open questions. One question was that of the definition of the Pettersson model. As I indicated previously this was not clear from the literature. My answer to the question is that this system should be treated as a system of DAE (differential-algebraic equations). In other words it can be written as a set of ODE $\dot x=f(x,y)$ coupled to a set of algebraic equations $g(x,y)=0$. In general it is not clear that this type of system is locally well-posed. In other words, given a pair $(x_0,y_0)$ with $g(x_0,y_0)=0$ it is not clear whether there is a solution $(x(t),y(t))$ of the system, local in time, with $x(0)=x_0$ and $y(0)=y_0$. Of course if the partial derivative of $g$ with repect to $y$ is invertible it follows by the implicit function theorem that $g(x,y)=0$ is locally equivalent to a relation $y=h(x)$ and the original system is equivalent to $\dot x=f(x,h(x))$. Then local well-posedness is clear. The calculations in the 1988 paper of Pettersson and Ryde-Pettersson indicate that this should be true for the Pettersson model but there are details missing in the paper and I have not (yet) been able to supply these. The conservative strategy is then to stick to the DAE picture. Then we do not have a basis for studying the dynamics but at least we have a well-defined system of equations and it is meaningful to discuss its steady states.

I was able to prove that there are parameter values for which the Pettersson model has at least two distinct positive steady states. In doing this I was helped by an earlier (1987) paper of Pettersson and Ryde-Pettersson. The idea is to shut off the process of storage as starch so as to get a subnetwork. If two steady states can be obtained for this modified system we may be able to get steady states for the original system using the implicit function theorem. There are some more complications but the a key step in the proof is the one just described. So how do we get steady states for the modified system? The idea is to solve many of the equations explicitly so that the problem reduces to a single equation for one unknown, the concentration of DHAP. (When applying the implicit function theorem we have to use a system of two equations for two unknowns.) In the end we are left with a quadratic equation and we can arrange for the coefficients in that equation to have convenient properties by choosing the parameters in the dynamical system suitably. This approach can be put in a wider context using the concept of stoichiometric generators but the proof is not logically dependent on using the theory of those objects.

Having got some information about the Pettersson model we may ask what happens when we go over to the Poolman model. The Poolman model is a system of ODE from the start and so we do not have any conceptual problems in that case. The method of construction of steady states can be adapted rather easily so as to apply to the system of DAE related to the Poolman model (let us call it the reduced Poolman model since it can be expressed as a singular limit of the Poolman model). The result is that there are parameter values for which the reduced Poolman model has at least three steady states. Whether the Poolman model itself can have three steady states is not yet clear since it is not clear whether the transverse eigenvalues (in the sense of GSPT) are all non-zero.

By analogy with known facts the following intuitive picture can be developed. Note, however, that this intuition has not yet been confirmed by proofs. In the picture one of the positive steady states of the Pettersson model is stable and the other unstable. Steady states on the boundary where some concentrations are zero are stable. Under the perturbation from the Pettersson model to the reduced Poolman model an additional stable positive steady state bifurcates from the boundary and joins the other two. This picture may be an oversimplification but I hope that it contains some grain of truth.

### A visit to Iceland

September 4, 2016

I just returned from 10 days as a tourist in Iceland. It was not my first time there. Years ago I went on a cruise which included two stops in Iceland, one in Reykjavik and one in Akureyri. In each case there was a short bus tour to see some typical sights – a waterfall, a geysir and a volcanic region with bubbling mud and hot springs. This time I had a chance to see a lot more. I enjoyed the cruise a lot but I had the impression that the majority of the people on the ship were very bored. The main antidote to the boredom offered was lots of food. One day I got up from the dinner table and went on deck. There had been no indication that there might be something interesting to see. When I opened the door I was confronted with a beautifully conical volcano covered with ice, Snaefellsjökull. (I will come back to the interesting issue of Icelandic pronuciation later.) This was one of my strongest impressions from the whole cruise. The volcano is at the end of a long peninsula to the north of Reykjavik. This time I learned that this volcano is the esoteric centre of Iceland and that it was the starting point of Jules Verne’s Journey to the Centre of the Earth. This was not really a point on the programme of the tour this time but it was clearly visible with binoculars from the hotel in Rekjavik where we spent the last two nights. I had one view of it which was monochrome due to the light conditions but where the sharp edges of the crater stood our clearly.

One attraction of Iceland for me was the bird life. It seems that the country has claimed exclusive rights on the puffin. The numerous tourist shops in Reykjavik are called ‘puffin shops’ due to the number of representations of that bird they sell. I also saw puffin offered as one of the constituents of a special menu also including whale and horse meat. We spent one night in Vik and I discovered two stranded fulmars on a grass area not far from the hotel. These birds can only take off from an elevated starting point like a cliff or from water. If one lands on a flat area some distance from the sea then it is doomed unless it gets help. I rescued two of them by carrying them (ten minutes walk including crossing a road with significant traffic) to the sea. Since there had not been a big storm I suppose they had come down during their first flight after leaving the nest. (There were fulmars nesting on inland cliffs on the other side of the hotel from the sea.) Fortunately I still knew how to catch them and pick them up without hurting them or being the victim of their defence mechanism of spitting foul-smelling oil when feeling threatened. I enjoyed seeing a few glaucous gulls in the harbour in Reykjavik on the last day. Probably the last time I saw any was on the cruise I already mentioned. It was also nice to see and hear many whimbrels. The first one already welcomed me at the airport when I arrived.

I felt at home in the natural surroundings in Iceland and after a few days I thought of one explanation. There are very few trees in Iceland and this is just as it is in Orkney where I grew up. The first time I was on the mainland of Scotland when I was four years old I said ‘I don’t like this place – you can’t see anything for trees’. There are many areas in Iceland where there is only sand, rocks, water and ice. I had the impression of seeing what the Earth is really like, without the veil of green which we usually see. I also got an impression of what it is really like to live next to a volcano. I was in a museum close to (and devoted to) Eyafjallajökull, the infamous producer of ash with the complicated name. I learned that one US journalist just called it E15, due to the number of letters. There was a film showing in the museum explaining what people living near the volcano experienced at the time of the last eruption. Coming back to the name, the pronunciation of Icelandic does seems to be a difficult question but also an interesting one. I would like to spend some time understanding it better. There are nice videos on the pronuciation of Eyafjallajökull here and here. The final double l is the really tricky point. There are points of similarity between the Icelandic language and the dialect I grew up with. This is due to the influence of an extinct language called Norn which was spoken on Orkney and Shetland in past centuries and which is related to (Old) Icelandic. For instance the oystercatcher is called tjaldur in Icelandic and chaldro in our dialect.

I also had some culinary experiences. At breakfast in the hotels there was always a bottle of cod liver oil on the table. I remember this liquid from my childhood as a threat used on young children. ‘If you do not behave yourself I will give you a spoonfull of cod liver oil.’ Due to persistent encouragement from Eva I tried a little and found it not as bad as I expected. Our guide also gave us some pieces of Greenland shark to try. He gave  us a warning about the taste and some of the alcholic drink called the black death to wash it down with. It tastes of nothing at first but chewing leads to a strong taste reminiscent of urine. In fact the flesh of the shark is poisonous due to its content of trimethylamine N-oxide. In Iceland it is treated by first burying it for several weeks and then drying it to get rid of the poison. The result is considered a delicacy. The Greenland shark is interesting because of the fact that it was recently discovered that it can live to be four hundred years old, only becoming sexually mature when it is 150. I want to read more about it.

As a final comment on Iceland: the weather was much better than we expected!