## Archive for May, 2009

### H1N1 and the influenza pandemic of 1918

May 15, 2009

A few years ago I read the book ‘Flu. The story of the great influenza pandemic of 1918 and the search for the virus that caused it’ by Gina Kolata. (Actually it happened to be the German translation.) I found it very interesting and a pleasure to read. The recent public interest in the outbreak of influenza of type H1N1 in Mexico led me to take up the book again. I found it just as fascinating as the first time around and I ended up rereading the whole book. Things I had learned in the meantime allowed me to appreciate more aspects of the subject. In what follows I will describe some of the highlights.

The main subject of the book is the influenza pandemic of 1918. According to conservative estimates this killed 50 million people, more than died in combat in the First World War. In view of the magnitude of the catastrophe it is surprising that it is not more widely known. In 1951 Johan Hultin travelled to Brevig in Alaska and obtained samples from the remains of victims from 1918 which had been relatively well preserved in the permafrost.He had hoped that the virus might have survived but this was too optimistic. He could not do much with his samples at that time. Later it was clear to him that with more recent developments in molecular biology there were new possibilities of using this kind of material. Independently of this, in 1995 Jeffery Taubenberger and his colleagues at the Armed Forces Institute of Pathology started to try to obtain information about the 1918 influenza virus from remains of soldiers who had died at that time which were archived at the institute. They were able to determine part of the genetic sequence of the virus but the quantity of material they had was so small as to limit the possibilities. Hultin read their first publication on the subject in Science in 1997 and contacted Taubenberger, offering to return to Brevig to obtain more material. He was successful and this finally allowed Taubenberger’s team to determine the whole genome of the virus. This was completed in 2005. A few months later the virus was reconstructed at the Centers for Disease Control and Prevention (CDC).

There were two parts of the book which I liked less. This was not because the writing was any less good in those parts – what I did not like was aspects of the content. The first of these two parts concerned the fears of a pandemic in 1976 and the reactions to it. At that time a mass vaccination was carried out which was very expensive and probably not necessary. This just shows how difficult decision making can be in this kind of situation. The thing which I find disturbing is that the costs of this were dwarfed by a sum of over three billion dollars which the government had to pay to people who claimed to have suffered adverse consequences from being vaccinated. This is of course likely to affect decisions of this kind in the future. My conclusion
from this is that the worst virus is probably less dangerous than the mechanisms which take place within human society and prevent mankind from reacting to the threat of a virus in the most effective way. The second part concerns another expedition to obtain material from the influenza victims of 1918, this time in Spitzbergen. It was the idea of Kirsty Duncan. Here I want to describe my personal reactions. From the beginning I felt admiration for the efforts of Hultin and of Taubenberger and his team. In contrast, my attitude to Kirsty Duncan was immediately negative. The sequel only strengthened this impression. The expedition set up by Duncan was a failure – that could have happened to anyone. What I dislike most is the combination of a facade of integrity with the refusal to admit the truth. I find it impressive when people achieve something remarkable by working discretely and quietly rather than thriving on and exploiting publicity. I am happy that in this case luck was on the side of those who deserved it.

One interesting effect of the affair concerning the pandemic scare and the vaccination campaign of 1976 was that the idea came up that a rare side effect of the vaccination might be the disease called Guillain-Barre syndrome. This is a demyelinating disease of the peripheral nerves. It seems that at least some types of this disease are related to molecular mimicry, a subject mentioned in a previous post. In this case the disease can be triggered by the bacterium Campylobacter pylori. Perhaps this disease could be a valuable model for autoimmunity in general.

The progress of the present H1N1 epidemic can be followed in daily reports on the web page of the World Health Organization. Today (15th May) the official number of cases is 7520.

### Dynamics of dendritic cells

May 11, 2009

On 23.04 I heard a talk by Michel Nussenzweig from Rockefeller University. His subject was dendritic cells, a class of white blood cells. For the casual observer, such as myself, it might seem that the class is homogeneous. It was emphasized by Nussenzweig that this is far from being the case. According to him, dendritic cells come in various types and the problem of classification may be as complicated as it is in the case of their more prominent relatives, the T-cells. As mentioned in previous posts, for the latter distinctions are made between CD4+, CD8+, Th1, Th2, Th17 etc. In the meantime various classes of dendritic cells have been recognized and it seems that not distinguishing between them sufficiently carefully has been an obstacle to progress. There are, for instance, conventional dendritic cells (cDC) and plasmacytoid dendritic cells (pDC). A related issue is insufficient precision in the use of language. As an aside: a ‘follicular dendritic cell’ is something quite different from a dendritic cell in the strict sense, sharing no more with it than its name and its morphology when seen under the microscope.

Among the themes of the talk were the questions of which cells occur in the course of development of dendritic cells from hematopoietic stem cells, where the different steps of this development take place (in bone marrow, blood, lymphatic organs or other tissues) and the relations between these precursor cells and the corresponding stages in the development of other classes of cells such as macrophages. One tool which can be used to investigate these things is parabiosis, where the bloodstreams of two mice are joined together.

At one point in the talk the speaker said, ‘Here we use a bit of mathematics’. He did not say what kind of mathematics. I sometimes have the impression in talks by biologists for biologists that the feeling is that it would be impolite to the audience, if not indecent, to show any mathematics. In this case I decided to look into what the mathematical content really is. For this I looked at the paper ‘Origin of dendritic cells in peripheral lymphoid organs of mice’ (Nature Immunology 8, 578) where Nussenzweig is one of the authors. The mathematics is not in the main text – to see it is necessary to go to the “Supplementary Methods” available as a separate file in the online version of the paper. From the point of view of a mathematician the presentation of the mathematical formulae is not very convenient. For instance, an ODE like $\frac{df}{dt}=g$ would be written as $df=g^*dt$. For me the first step in understanding the mathematical part was to convert the equations into TeX. This having been done, equations are:
$\frac{dN}{dt}=\left(\frac{V}{C}-D+P\right)N$
$\frac{dM}{dt}=\left(\frac{2V}{C}+PQ\right)N-\left(\frac{V}{C}+D\right)M$
$\frac{dL}{dt}=\frac{3PN}{10}+\left(\frac{V}{C}-D\right)L$
Here $N$, $M$ and $L$ are functions of time while the other quantities denoted by capital letters are constant parameters. The first equation is decoupled from the others and in fact plays a different role. $N$ is the number of cDC in the spleen and is taken to be $10^6$. Thus the left hand side of the first equation is assumed to vanish and this gives the relation $D=\frac{V}{C}+P$. Taking account of this, there remains a system of two linear ODE, which can easily be solved explicitly. The resulting solution can be used to determine the parameters in terms of experimental data. A question of interest is how many of the cells have divided in a certain time interval. This can be investigated experimentally by adding the nucleoside analogue bromodeoxyuridine (BrdU). When a cell divides this compound is incorporated into the DNA of the daughter cells. Thus an assay of BrdU can be used to measure the proportion of cells which have divided. At this point it is appropriate to explain the meaning of the variables $M$ and $N$.The variable $M$ is the proportion of cDC which are labelled with BrdU at a given time. $L$ is the proportion of cDC in the mouse under consideration which come from the other mouse joined to it by parabiosis.

The experimental data is as follows. The proportion of cDC in the spleen which are dividing is 5 per cent. This is the quantity $V$ in the equations. At the initial time there are no cells labelled by BrdU ($M(0)=0$) and no cells coming from the other mouse ($L(0)=0$).
After 2.2 days 50% of the cells have taken up BrdU. If ‘days’ is taken as the unit of time then this gives $M(2.2)=(0.5)N$. On long time scales this proportion approaches 91%, so that $\lim_{t\to\infty}M(t)=(0.91)N$. After 13 days the proportion of cDC from the other mouse is 22% ($L(13)=(0.22)N$) while on long time scales it is 30% ($\lim_{t\to\infty}L(\infty)=(0.3) N$). Putting this information into the explicit solution of the equations and doing some elementary algebra allows all parameters to be computed. In particular $P=0.101673$. This is the proportion of the cDC in the spleen which enter from the blood in unit time.This can be converted to the number of cDC which enter the spleen each hour by multiplying by $10^6\times (1/24)$. The result is 4236 cells per hour, a figure which, rounded up to ‘nearly 4300’, is quoted in the abstract of the paper.

The modest goal of this discussion has been to obtain an answer to the question, ‘What is the mathematical content involved in this work’.