## Archive for the ‘diseases’ Category

### Uğur Şahin, Özlem Türeci and The Vaccine

October 4, 2021

I now come to the story itself. Şahin and Türeci are both Germans whose parents came to Germany from Turkey. They studied medicine and they met during the practical part of their studies. They were both affected by seeing patients dying of cancer while medicine was helpless to prevent it. They decided they wanted to change the situation and have pursued that goal with remarkable consistency since then. They later came to the University of Mainz. They founded a biotechnology company called Ganymed producing monoclonal antibodies which was eventually sold for several hundred million Euros. They then went on to found BioNTech with the aim of using mRNA technology for cancer immunotherapy. An important role was played by money provided by the Strüngmann brothers. They had become billionaires through their company Hexal which sold generic drugs. They were relatively independent of the usual mechanisms of the financial markets and this was a big advantage for BioNTech. (A side remark: I learned from the book that the capital NT in the middle of the company name stands for ‘new technology’.) In early January 2020 Şahin foresaw the importance of COVID-19 and immediately began a project to apply the mRNA technology of BioNTech to develop a vaccine. The book is the story of many of the obstacles which he and Türeci had to overcome to attain this goal. In the US the vaccine is associated with the name Pfizer and it is important to mention at this point what the role of Pfizer was, namely to provide money and logistics. The main ideas came from Şahin and Türeci. Of course no important scientific development is due to one or two people alone and there are many contributions. In this case a central contribution came from Katalin Karikó.

How does the BioNTech vaccine work? The central idea of an mRNA vaccine is as follows. The aim is to introduce certain proteins into the body which are similar to ones found in the virus. The immune response to these proteins will then also act against the virus. What is actually injected is mRNA and that is then translated into the desired proteins by the cellular machinery. To start with the sequences of relevant proteins must be identified and corresponding mRNA molecules produced in vitro based on a DNA template. The RNA does not only contain the code for the protein but also extra elements which influence the way in which it behaves or is treated within a cell. In addition it is coated with some lipids which protect it from degradation by certain enzymes and help it to enter cells. Karikó played a central role in the development of this lipid technology. After the RNA has been injected it has to get into cells. A good target cell type are the dendritic cells which take up material from their surroundings by macropinocytosis. They then produce proteins based on the RNA template, cut them up into small peptides and display these on their surface. They also move to the lymph nodes. There they can present the antigens to T cells, which get activated. For T cells to get activated a second signal is also necessary and it is fortunate that mRNA can provide such a signal – in the language of vaccines it shows a natural adjuvant activity. In many more popular accounts of the role of the immune system in the vaccination against COVID-19 antibodies are the central subject. In fact according to the book many vaccine developers are somewhat fixated on antibodies and underestimate the role of T cells. There Şahin had to do a lot of convincing. It is nevertheless the case that antibodies are very important in this story and there is one point which I do not understand. Antibodies are produced by B cells and in order to do so they must be activated by the antigen. For this to happen the antigen must be visible outside the cells. So how do proteins produced in dendritic cells get exported so that B cells can see them?

I admire Şahin and Türeci very much. This has two aspects. The first is their amazing achievement in producing the vaccine against COVID-19 in record time. However there is also another aspect which I find very important. It is related to what I have learned about these two people from the book and from other sources. It has to do with a human quality which I find very important and which I believe is not appreciated as it should be in our society. This is humility. In their work Şahin and Türeci have been extremely ambitious but it seems to me that in their private life they have remained humble and this makes them an example to be followed.

### My COVID-19 vaccination, part 2

August 5, 2021

Since my last post on this subject a few things have changed. In Germany 53% of people are fully vaccinated against COVID-19, which is good news. We are now in a situation where in this country any adult who wants the vaccination can get it. Of course this percentage is still a lot lower than what is desirable and the number of people being vaccinated per day has dropped to less than half what it was in mid June. I find it sad, and at the same time difficult to understand, that there are so many people who are not motivated enough to go out and get the vaccination.

Yesterday my wife and I got our second vaccination. In the meantime the relevant authority (STIKO) has recommended that those vaccinated once with the product of AstraZeneca should get an mRNA vaccine the second time. The fact that we waited the rather long time suggested to get our second injection meant that the new recommendation had already come out and we were able to get the vaccine of Biontech the second time around. There have not been many studies of the combination vaccination but as far as I have seen those that there are gave very positive results. So we are happy that it turned out this way. This time the arm where I got the injection was sensitive to pressure during the night but this effect was almost gone by this morning. The only other side effect I noticed was an increased production of endorphins. In other words, I was very happy to have reached this point although I know that it takes a couple of weeks before the maximal protection is there.

Every second year there is an event in Mainz devoted to the popularization of science called the Wissenschaftsmarkt. It has been taking place for the last twenty years. Normally it is in the centre of town but due to the pandemic it will be largely digital this year. This year it is on 11th and 12th September and has the title ‘Mensch und Gesundheit’ [rough translation: human beings and their health]. I will contribute a video with the title ‘Gegen COVID-19 mit Mathematik’ [against COVID-19 with mathematics]. The aim of this video is to explain to non-scientists the importance of mathematics in fighting infectious diseases. I talk about what mathematical models can contribute in this domain but also, which is just as important, about what they cannot do. If the public is to trust statements by scientists it is important to take measures against creating false expectations. I do not go into too much detail about COVID-19 itself since at the moment there is too little information available and too much public controversy. Instead I concentrate on an example from long ago where it is easier to see clearly. It also happens to be the example where the basic reproductive number was discovered. This is the work of Ronald Ross on the control of malaria. Ross was the one who demonstrated that malaria is transmitted by mosquito bites and he was rewarded for that discovery with a Nobel Prize in 1902. After that he studied ways of controlling the disease. This was for instance important in the context of the construction of the Panama Canal. There the first attempt failed because so many workers died of infectious diseases, mainly malaria and yellow fever, both transmitted by mosquitos. The question came up, whether killing a certain percentage of mosquitos could lead to a long-term elimination of malaria or whether the disease would simply come back. Ross, a man of many talents, set up a simple mathematical model and used it to show that elimination is possible and was even able to estimate the percentage necessary. This provided him with a powerful argument which he could use against the many people who were sceptical about the idea.

### Paper on hepatitis C

November 13, 2020

Together with Alexis Nangue and other colleagues from Cameroon we have just completed a paper on mathematical modelling of hepatitis C. What is being modelled here is the dynamics of the amount of the virus and infected cells within a host. The model we study is a modification of one proposed by Guedj and Neumann, J. Theor. Biol. 267, 330. One part of it is a three-dimensional model, which is related to the basic model of virus dynamics. It is coupled with a two-dimensional model which gives a simple description of the way in which the virus replicates inside a host cell. This intracellular process is related to the mode of action of the modern drugs used to treat hepatitis C. I gave some information about the disease itself and its treatment in a previous post. In the end the object of study is a system of five ODE with many parameters.

For this system we first proved global existence and boundedness of the solutions, as well as positivity (positive initial data lead to a positive solution). One twist here is a certain lack of regularity of the coefficients of the system. When some of the unknowns become zero the right hand side of the equations is discontinuous. This means that it is necessary to prove that this singular set is not approached during the evolution of a positive solution. The source of the irregularity is the use of something called the standard incidence function instead of simple mass action kinetics. The former type of kinetics has a long history in epidemiology and I do not want to try to explain the background here. In any case, there are arguments which say that mass action kinetics leads to unrealistic results in within-host models of hepatitis and that the standard incidence function is better.

We show that the model has up to two virus-free steady states and determine their stability. The study of positive steady states is more difficult and, at the moment, incomplete. We have proved that there cannot be more than three steady states but we do not know if there is ever more than one. Under increasingly restrictive assumptions on the parameters (restrictions which are unfortunately not all biologically motivated) we show that there is at least one positive steady state, that there is exactly one and that that one is asymptotically stable. Under certain other assumptions we can show that every solution converges to a steady state. This last proof uses the method of Li and Muldowney discussed in a previous post. Learning about this method was one of the (positive) side effects of working on this project. Another was an improvement of my understanding of the concept of the basic reproductive number as discussed here and here. During this project I have learned a lot of new things, mathematical and biological, and I feel that I am now in a stronger position to tackle other projects modelling hepatitis C and other infectious diseases.

This

### Talk by David Ho on COVID-19

August 22, 2020

On Thursday David Ho gave a keynote lecture at the SMB conference. He talked about work to develop monoclonal antibodies against SARS-CoV-2. He started by apologising, in view of the given audience, that there would be no mathematics in his talk but he did make make clear his continuing belief in the importance of applying mathematics to biology. He has been leading an effort with a precise medical goal – to find effective neutralising antibodies against this new virus. Antibodies were obtained from five patients severely ill with COVID-19. Four of them survived while one later died of the disease. These antibodies were then analysed by biochemical and bioinformatic means to find those which bound best to the spike protein of the virus. In this context I learned some basic things about the virus. The spike, which is used by the virus to enter cells is considered the number one target for antibodies which could be effective in combating the disease. More precisely there are two different subdomains which are possible targets, one more at the tip of the spike (the receptor-binding domain) and another more on the sides (the N-terminal domain), which is a trimer. A number of antibodies were found which bind to the first subdomain or to one of the subunits of the second. Another was found whose binding site is somewhat less local. This whole process was carried out in just few weeks, a remarkable achievement.

The antibodies just mentioned are the therapeutic candidates. The idea is to either produce monoclonal antoibodies with these sequences or possibly versions which are improved so as to be longer-lived. Monoclonal antibodies are known to be extremely expensive when used to treat other diseases, such as cancer. They are also expensive in the present context, but the speaker said that the retail cost depends very much on the quantity produced. In other applications the number of patients is relatively small and the cost correspondingly high. If the antobodies were being used for a very large number of patients the cost would be lower. It would remain problematic for low and middle income countries. It has been discussed that the Gates foundation might make it possible to offer this treatment in poorer countries for fifty dollars a dose. The main advantage of this method compared with that of trying to use antibodies from the serum of patients directly is that it is much more practical to apply on a very large scale. The effectiveness of the antibodies against the disease has been tested in hamsters. Ho made the impression of someone tackling a major problem of humanity head on with some of the best tools available. He said that an article giving an account of the work had appeared in Nature (Potent neutralizing antibodies against multiple epitopes on SARS-CoV-2 spike, Nature 584, 450). In response to one question on one aspect of the treatment he said that the answer was not known but he would just be continuing to a Zoom meeting of researchers leading the attempts to develop therapies which was to discuss exactly that question.

### The basic reproduction number for infectious diseases, part 2

July 9, 2020

Here I continue the discussion of the previous post. There I mentioned that when defining a basic reproduction number it is necessary, in addition to defining a set of ODE, to make a choice of infected and uninfected compartments. This means partitioning the unknowns into two subsets. In addition it is necessary to distinguish processes regarded as new infections from others. This means splitting the right hand side of the equations into a sum of two terms. There are also some other biologically motivated assumptions on the right hand side. As indicated in the previous post, a reproduction number is a feature of a disease-free steady state of the model (i.e. a steady state where the unknowns belonging to the infected compartment are zero). In fact it is a feature of the linearization of the model about that point. Intuitively, it has to do with a situation where a population contains a very small number of infected individuals. The matrix defining the right hand side of the linearization is a sum of two terms, each of which is partitioned in a certain way. We now consider a situation where the disease-free steady state is perturbed by introducing a small number of individuals into each of the infected compartments while supposing that they cannot cause a significant number of secondary infections. The numbers of individuals in the infected compartments then satisfy a linear system. Under the given assumptions all eigenvalues of the matrix defining this system have negative real parts. Thus the solution tends to zero exponentially. We are interested in the average number of individuals in these compartments over all positive times. To understand this consider first the simpler example of a single compartment with an exponential behaviour $x(t)=x_0e^{-at}$. The average value of $x$ is $\int_0^\infty x_0e^{-at}dt=\left[-a^{-1}x_0e^{-at}\right]_0^\infty=x_0a^{-1}$. In fact what we are interested in is the number of infections expected from the individuals in the infectious compartment. We have the equation $\psi'(t)=-V\psi (t)$, where all eigenvalues of $V$ have positive real parts and we want to calculate $F\int_0^\infty e^{-Vt}dt=FV^{-1}\psi (0)$, where $F$ describes the process of new infections. The matrix $FV^{-1}$ is the next generation matrix mentioned in the previous post. It is now a matter of some rather involved linear algebra to show that the modulus of the largest eigenvalue of this matrix is greater than one if and only if the greatest real part of an eigenvalue of the linearization of the system of ODE is greater than zero.

In the current reporting of epidemiological data the quantity $R$ is time-dependent. I am far away from being able to link this with the above discussion. I looked at the web page of the Robert Koch Institute to see what they say about how they produce their curves. This led me to a paper of Cintron-Arias et al. (Math. Biosci. Eng. 6, 261), which might be able to provide a gateway into this but it is clear that it involves many things which I do not understand at present. Perhaps I should first look at the classic book ‘Infectious Diseases of Humans’ by Anderson and May. Robert May died in April 2020 so that he did not have the opportunity to observe the present pandemic.

### The basic reproduction number for infectious diseases

June 12, 2020

These days reproduction numbers for epidemiology are prominent in the popular media. Many people are familiar with the idea that stopping a resurgence of COVID-19 infections in a region has to do with making and keeping something called $R$ less than one. They may also be familiar with the informal definition of $R$ that it is the number of new infections caused by an infected individual. But how is $R$ (or $R_0$ as it is more commonly called by scientists) defined? A mathematician might not expect to find an answer in the media but it might be reasonable to expect one in the scientific literature on epidemiology. In the past I have been frustrated by the extent to which this fails to be the case. What is typically given is a description in words which I never found possible to convert into a precise mathematical account, despite considerable effort. Now, in the context of a project on hepatis C which I have been working on with colleagues from Cameroon, my attention was drawn to a paper of van den Driessche and Watmough (Math. Biosci. 180, 29) which contains some answers of the type I was looking for. I was vaguely aware of this paper before but I had never seriously tried to read it because I did not realise its nature.

The context in which I would have liked to find answers is that of models given by systems of ordinary differential equations where the unknowns are the numbers of individuals in different categories (susceptible, infected, recovered etc.) as functions of time. How the numbers reported in the media are calculated (on the basis of discrete data) is something I have not yet tried to find out. At the moment I would like an answer in the context which bothered me in the past and this is the context treated in the paper mentioned above. A typical situation is that found in the basic model of virus dynamics, a system of three ODE describing the dynamics of a virus within a host, with the unknowns being uninfected cells, infected cells and virions. There is a quantity $R_0$ which can be expressed in terms of the coefficients of the system. If $R_0\le 1$ then the only non-negative steady state is virus-free. This is the uninfected state and it is globally asymptotically stable. If $R_0>1$ there is an uninfected state which is unstable and an infected state which is positive and globally asymptotically stable. This kind of situation is not unique to this example and similar things are seen in many models of infection. There is a reproductive number (or perhaps more than one) which defines a threshold between different types of late-time behaviour.

It is not obvious that the analysis of van den Driessche and Watmough applies to models of in-host dynamics of a pathogen since it is necessary to make a choice of infected and uninfected compartments which is related to the biological interpretation of the variables and not just to the mathematical structure of the model. Their analysis does apply to the basic model of virus dynamics if the infected compartments are chosen to be the infected cells and virions and the reaction fluxes are partitioned in a suitable way. The simple picture of the significance of the reproductive number given above does not always hold. There is also another scenario which can occur and does so in many practical examples and involves the notion of a backward bifurcation. It goes as follows. For $R_0$ sufficiently small the disease-free steady state is globally asymptotically stable but as $R_0$ is increased this property breaks down before $R_0=1$ is reached. A fold bifurcation occurs which creates a stable and an unstable positive steady state. The unstable steady state moves so as to meet the disease-free state when $R_0=1$. For $R_0>1$ there are exactly two steady states and the positive one is globally asymptotically stable. There is bifurcation for $R_0=1$ but it has a different structure from that in the classical scenario (which is a transcritical bifurcation). It bears some resemblance to a sub-critical Hopf bifurcation.

The most useful insights I got from reading and thinking about the paper of van den Driessche and Watmough are as follows. The primary significance of $R_0$ concerns the disease-free steady state and its stability. The fact that it can sometimes characterise the stability of an infected steady state is a kind of bonus which does not apply to all models. What it can do is to provide information about the stability of a positive steady state in a regime where it is close to the bifurcation point where it separates from the disease-free steady state. This circumstance is analysed in the paper using centre manifold theory. The significance for the stability of a steady state which is far away is a weak one. Continuity arguments can be used to propagate information about stability through parameter space but only as long as no bifurcations happen. When this is the case depends on the details of the particular example being considered. What is the definition of $R_0$ given in the paper? It is the largest modulus of an eigenvalue of a certain matrix (the next generation matrix) constructed from the linearization of the system about the disease-free steady state, whereby the construction of this matrix incorporates information about the biological meaning of the variables. Consider the example of the basic model of virus dynamics with the choices of infected and uninfected compartments as above. There is more than way of partitioning the reaction fluxes. I first tried to put both the production of infected cells and the production of virions into the category of fluxes called $\cal F$ in the paper. Applying the definition of the reproduction number given there leads to $\sqrt{R_0}$, where $R_0$ is the reproduction number usually quoted for this model. If instead only the production of infected cells is put into the category $\cal F$ then the general definition gives the conventional answer $R_0$. The two quantities defining the threshold are different but the definition of being above or below the threshold are the same. ($\sqrt{x}<1\Leftrightarrow x>1$). That this kind of phenomenon can occur is shown by example in the paper.

### The plague priest of Annaberg

March 26, 2020

I find accounts of epidemics, whether documentary or fictional, fascinating. I appreciated texts of this kind by Camus (La Peste), Defoe (Journal of the Plague Year) and Giono (Le Hussard sur le Toit). This interest is reflected in a number of posts in this blog, for instance this one on the influenza pandemic of 1918. At the moment we all have the opportunity to experience what a pandemic is like, some of us more than others. In such a situation there are two basic points of view, depending on whether you see the events as concerning other people or whether you feel that you are yourself one of the potential victims. The choice of one of these points of view probably does not depend mainly on the external circumstances, except in extreme cases, and is more dependent on individual psychology. I do feel that the present COVID-19 pandemic concerns me personally. This is because Germany, where I live, is one of the countries with the most total cases at the moment, after China, Italy, USA and Spain. Every evening I study the new data in the Situation Reports of the WHO. The numbers to be found in the Internet are sometimes quite inconsistent. This can be explained by the time delays in reporting, the differences in the definitions of classes of infected individuals used by different people or organizations and unfortunately in some cases by poltically motivated lies. My strategy for extracting real information from this data is to stick to one source I believe to be competent and trustworthy (the WHO) and to concentrate on the relative differences between one day and the next and one country and another in order to be able to see trends. I find interesting the extent to which diagrams coming from mathematical models have found their way into the media reporting of this subject. Prediction is a high priority for many people at the moment.

Motivated by this background I started to read a historical novel by Gertrud Busch called ‘Der Pestpfarrer von Annaberg’ [the plague priest of Annaberg] which I got from my wife. The main character in the book is a person who really existed but many of the events reported there are fictional. Annaberg is a town in Germany, in the area called ‘Erzgebirge’, the literal English translation of whose name is ‘Ore mountains’. This mountain range lies on the border between Germany and the Czech republic. People were attracted there by the discovery of valuable mineral deposits. In particular, starting in the late fifteenth century, there was a kind of gold rush there (Berggeschrey), with the difference that the metal which caused it was silver rather than gold. My wife was born and grew up in that area and for this reason I have spent some time in Annaberg and other places close to there. The narrator of the book is Wolfgang Uhle, a priest in the Erzgebirge in the sixteenth century active in Annaberg during the outbreak of plague there. In fact in the end only a small part of the book concerns the plague itself but I am glad I read it. The author has created a striking picture of the point of view of the narrator, at a great distance from the modern world.

During Uhle’s first period as a priest there was a fire in a neighbouring village which destroyed many houses. He saved the life of a young girl, in fact a small child, who was playing in a burning house. Much to the amusement of the adults the girl said she would marry him when she was old enough. In fact she meant it very seriously and when she was old enough it did happen that after some difficulties she got engaged to him. The tragedy of Wolfgang Uhle is that he had a temper which was sometimes uncontrollable. Before the marriage took place he once got into a rage due to the disgraceful behaviour of the judge in his village. Unfortunately at that moment he was holding a large hammer in his hand. A young girl had asked him if a stone she had brought him was valuable. He had some knowledge of geology and he intended to use the hammer to break open the stone and find out more about its composition. In his sudden rage he hit the judge on the head with the hammer and killed him. He went home in a state of shock without any plan but his housekeeper brought him to flee over the border into Bohemia. He was sentenced to death in absentia and hid in the woods for five years. The girl who he was engaged to repudiated him, stamped on his engagement ring and quickly married another man. He partly lived from what he could find in nature, living at first in a cave. Later he started working together with a charcoal burner. I learned something about what that industry was like when I visited those woods myself a few years ago. Eventually he revealed his identity and had to leave.

In the woods he met a man who had got lost and asked him the way. The man wanted to go to Bärenstein, which is the town where my wife spent her childhood. He agreed to show him the way. The man told him that the plague had broken out in Annaberg and that the town was desperately searching for a priest to tend to the spiritual needs of the sick. Uhle decided that he should volunteer, despite the danger. He saw this as God giving him a chance to make amends for his crime. He wrote letters to the local prince and the authorities of the town. The prince agreed to grant him a pardon in return for his service as priest for the people infected with the plague. He then went to Annaberg and tended to the sick, without regard to the danger he was putting himself in. There is not much description of the plague itself in the book. There is a key scene where he meets his former love on her deathbed and it turns out that she had continued to love him and felt guilty for having abandoned him. Uhle survives the plague, gets a new position as a priest, marries and has children. This book was different from what I expected when I started reading it. Actually the fact that it was so different from things I otherwise encounter made it worthwhile for me to read it.

### SMB meeting in Montreal

July 27, 2019

This week I have been attending the SMB meeting in Montreal. There was a minisymposium on reaction networks and I gave a talk there on my work with Elisenda Feliu and Carsten Wiuf on multistability in the multiple futile cycle. There were also other talks related to that system. A direction which was new to me and was discussed in a talk by Elizabeth Gross was using a sophisticated technique from algebraic geometry (the mixed volume) to obtain an upper bound on the number of complex solutions of the equations for steady states for a reaction network (which is then of course also an upper bound for the number of positive real solutions). There were two talks about the dynamics of complex balanced reaction networks with diffusion. I have the impression that there remains a lot to be understood in that area.

At this conference the lecture rooms were usually big enough. An exception was the first session ‘mathematical oncology from bench to bedside’ which was completely overfilled and had to move to a different room. In that session there was a tremendous amount of enthusiasm. There is now a subgroup of the SMB for cancer modelling which seems to be very active with its own web page and blog. I should join that subgroup. Some of the speakers were so full of energy and so extrovert that it was a bit much for me. Nevertheless, it is clear that this is an exciting area and I would like to be part of it. There was also a session of cancer immunotherapy led by Vincent Lemaire from Genentech. He and two others described the mathematical modelling being done in cancer immunotherapy in three major pharmaceutical companies (Genentech, Pfizer and Glaxo-Smith-Kline). These are very big models. Lemaire said that at the moment that there are 2500 clinical trials going on for therapies related to PD-1. A recurring theme in these talks was the difference between mice and men.

This morning there was a talk by Hassan Jamaleddine concerning nanoparticles used to present antigen. These apparently primarily stimulate Tregs more than effector T cells and can thus be used as a therapy for autoimmune diseases. He showed some impressive pictures illustrating clearance of EAE using this technique. A central theme was interference between attempts to use the technique in animals with two autoimmune diseases in different organs, e.g. brain and liver. I was interested by the fact that for what he was doing steady state analysis was insufficient for understanding the biology.

This afternoon, the conference being over, I took to opportunity to visit Paul Francois at McGill, a visit which was well worthwhile.

### Book on cancer therapy using immune checkpoints, part 2

April 20, 2019

I now finished reading the book of Graeber I wrote about in the last post. Here are some additional comments. Chapter 7 is about CAR T cells, a topic which I wrote about briefly here. I also mentioned in that post that there is a mathematical model related to this in the literature but I have not got around to studying it. Chapter 8 is a summary of the present state of cancer immunotherapy while the last chapter is mainly concerned with an individual case where PD-1 therapy showed a remarkable success but the patient, while against all odds still alive, is still not cancer-free. It should not be forgotten that the impressive success stories in this field are accompanied by numerous failures and the book also reports at length on what these failures can look like for individual patients.

For me the subject of this book is the most exciting topic in medicine I know at the moment. It is very dynamic with numerous clinical studies taking place. It is suggested in the book that there is a lot of redundancy in this and correspondingly a lot of waste, financial and human. My dream is that progress in this area could be helped by more theoretical input. What do I mean by progress? There are three directions which occur to me. (1) Improving the proportion of patients with a given type of cancer who respond by modifying a therapy or replacing it by a different one. (2) Identifying in advance which patients with a given type of cancer will respond to which therapy, so as to allow rational choices between therapies in individual cases. (3) Identifying new types of cancer which are promising targets for a given therapy. By theoretical input I mean getting a better mechanistic understanding of the ways in which given therapies work and using that to obtain a better understanding of the conditions needed for success. The dream goes further with the hope that this theoretical input could be improved by the formulation and analysis of mathematical models.

What indications are there that this dream can lead to something real? I have already mentioned one mathematical model related to CAR T-cells. I have mentioned a mechanistic model for PD-1 by Mellman and collaborators here. This has been made into a mathematical model in a 2018 article by Arulraj and Barik (PLoS ONE 13(10): e0206232). There is a mathematical model for CTLA-4 by Jansson et al. (J. Immunol. 175, 1575) and it has been extended to model the effects of related immunotherapy in a 2018 paper of Ganesan et al. (BMC Med. Inform. Decis. Mak. 18,37).

I conclude by discussing one topic which is not mentioned in the book. In Mainz (where I live) there is a company called BIONTECH with 850 employees whose business is cancer immunotherapy. The CEO of the company is Ugur Sahin, who is also a professor at the University of Mainz. I have heard a couple of talks by him, which were on a relatively general level. I did not really understand what his speciality is, only that it has something to do with mRNA. I now tried to learn some more about this and I realised that there is a relation to a topic mentioned in the book, that of cold and hot tumours. The most favourable situation for immune checkpoint therapies is where a tumour does in principle generate a strong immune response and has adapted to switch that off. Then the therapy can switch it back on. This is the case of a hot tumour, which exhibits a lot of mutations and where enough of these mutations are visible to the immune system. By contrast for a cold tumour, with no obvious mutations, there is no basis for the therapy to work on. The idea of the type of therapy being developed by Sahin and collaborators is as follows (my preliminary understanding). First analyse DNA and RNA from the tumour of a patient to identify existing mutations. Then try to determine by bioinformatic methods which of these mutations could be presented effectively by the MHC molecules of the patients. This leads to candidate proteins which might stimulate the immune system to attack the tumour cells. Now synthesise mRNA coding for those proteins and use it as a vaccine. The results of the first trials of this technique are reported in a 2017 paper in Nature 547, 222. It has 295 citations in Web of Science which indicates that it has attracted some attention.

### Book on cancer therapy using immune checkpoints

April 19, 2019

In a previous post I wrote about cancer immunotherapy and, in particular, about the relevance of immune checkpoints such as CTLA-4. For the scientific work leading to this therapy Jim Allison and Tasuku Honjo were awarded the Nobel Prize for Medicine in 2018. I am reading a book on this subject, ‘The Breakthrough. Immunotherapy and the Race to Cure Cancer’ by Charles Graeber. I did not feel in harmony with this book due to some notable features which made it far from me. One was the use of words and concepts which are typically American and whose meanings I as a European do not know. Of course I could go out and google them but I do not always feel like it. A similar problem arises from the fact that I belong to a different generation than the author. It is perhaps important to realise that the author is a journalist and not someone with a strong background in biology or medicine. One possible symptom of this is the occurrence of spelling mistakes or unconventional names (e.g. ‘raff’ instead of ‘raf’, ‘Mederex’ instead of ‘Medarex’ for the company which played an essential role in the development of antibodies for cancer immunotherapy, ‘dendrites’ instead of ‘dendritic cells’). As a consequence I think that if a biological statement made in the book looks particularly interesting it is worth trying to verify it independently. For example, the claim in one of the notes to Chapter 5 that penicillin is fatal to mice is false. This is not only of interest as a matter of scientific fact since it has also been used as an (unjustified) argument by protesters against medical experiments in animals. More details can be found here.