Archive for April, 2019

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.

Despite this I find the book a very rewarding read due to the stories it tells. It was exciting to read the first chapter which describes the experiences of one of the first patients to experience what seemed like a miracle cure due to treatment with an antibody to PD-L1. I find it fascinating to get an impression of what a person in this type of situation actually lives through. On a personal note, I was happy to see that when the patient met the team of researchers who had developed the treatment one of the people present was Ira Mellman. As I mentioned in a previous post I have been present at a lecture of Mellman. The second chapter describes known cases where an infectious disease can lead to the elimination of a tumour. It describes how, more than a hundred years ago, William Coley tried to turn this observation into a therapy. His success in doing so was very limited and this was unavoidable. The ideas needed to understand what might be going on in such a situation simply did not exist at that time. Without understanding it was impossible to pursue a therapy in a controlled way. I knew something about this story before reading the book but it filled in a lot more background for me. The key figure in the third chapter is Steven Rosenberg. I had not heard his name before. He had an important position at the NIH and pursued research into cancer immunotherapy during a period where there were few returns. One substance which he tried to use therapeutically was IL-2. Here again I was pleased to come across the name of a person who I have heard give a talk, as mentioned in a previous post. This is Kendall Smith, the discoverer of IL-2.

Chapter four is concerned with Jim Allison, the discoverer of the first type of cancer immunotherapy using CTLA-4. I find it interesting that in his research Allison was not deriven by the wish to find a cancer therapy. He wanted to understand T cells and their activation. While doing so he discovered CTLA-4, as an important ‘off switch’ for T cells. It seems that from the beginning Allison liked to try certain experiments just to see what would happen. If what he found was more complicated than he expected he found that good. In any case, Allison did an experiment where mice with tumours were given antibodies to CTLA-4. This disables the off switch. The result was that while the tumours continued to grow in the untreated control mice they disappeared in the treated mice. The 100% reponse was so unexpected that Allison immediately repeated the experiment to rule out having made some mistake. The result was the same.

The fifth chapter throws some light on the question why researchers were so sceptical for so long about the idea that the immune system can effectively fight cancer. The central conceptual reason is that in order to interpret the results of certain experiments it is not enough to consider the typical cancer cell. Instead it is necessary to think on a population level and see the tumour as an ecosystem. When cancer cells are attacked in some way and the majority die there will be a few left over which are immune to that particular type of attack. That small population will then expand and the tumour will grow again. The genetic composition of a typical cell in the new tumour will be very different from that of the old one. In the case of an attack by the immune system this gives rise to the concept of ‘cancer immunoediting’. On the road to transforming the experimental results of Allison into a therapy there were further conceptual obstacles along the road. In the phase 2 clinical trial for an antibody against CTLA-4 run by Bristol-Myers-Squibb (which had taken over the company Medarex which had started the development of the drug) the criteria for success were badly chosen. They were based on what might have been good criteria for a chemotherapy but were not good for the new type of therapy. Success was based on the tumours of a certain percentage of patients having shrunk by a certain amount after three months. The problem was that the time scale (which had been chosen to limit the expense) was too short and tumour size was not the right thing to look at. It could be seen that he tumours of certain patients had grown but they reported that they were feeling better. It happened that a patient who was about to die called up months later, after the planned endpoint of the trial and said ‘I’m fine’. What is the explanation for these things? The first aspect is that the immune response required to attack the tumour takes a considerable time to develop and success needs more than three months. The other is that a bigger tumour does not necessarily mean more cancer cells. It can also mean that there are huge numbers of immune cells in the tumour. Imaging the size of the tumour misses that. A similar trial to that of BMS gave similar results and was abandoned. That the same did not happen with the BMS trial was apparently due to someone called Axel Hoos. He persuaded the company to extend the trial and introduced a better endpoint criterion, the proportion of patients who live for a certain time. This led to success and eventually to the approval of the drug ipilimumab. Its rate of success, in the case of metastatic melanoma, is that about 20% of the patients are cured (in the sense that the tumours go away and have not come back until today, the survival curve flattens out at a positive value). The side effects are formidable, due to autoimmune reactions.

Chapter six comes back to the therapy with PD-L1 with which the book started. The treatments with antibodies against PD-1 and PD-L1 have major advantages compared to those with CTLA-4. The success rate with metastatic melanoma can exceed 50% and the side effects are much less serious. The latter aspect has to do with the fact that in this case the mode of action is less to activate T cells in general than to sustain the activation of cells which are already attacking the tumour. This does not mean that treatments targetting CTLA-4 have been superceded. For certain types of cancer it can be better than those targetting PD-1 or PD-L1 and combinations may be better than either type of therapy alone. For the second class of drugs getting them on the market was also not easy. In the book it is described how this worked in the case of a drug developed by Genentech. It had to be decided whether the company wanted to develop this drug or a more conventional cancer therapy. The first was more risky but promised a more fundamental advance if successful. There was a showdown between the oncologists and the immunologists. After a discussion which lasted several hours the person responsible for the decision said ‘This is enough, we are moving forward’ and chose the risky alternative.

This post has already got quite long and it is time to break it off here. What I have described already covers the basic discussion in the book of the therapies using CTLA-4 and PD-1 or PD-L1. I will leave everthing else for another time.

Banine’s ‘Jours caucasiens’

April 11, 2019

I have just read the novel ‘Jours caucasiens’ by Banine. This is an autobiographical account of the author’s childhood in Baku. I find it difficult to judge how much of what she writes there is true and how much is a product of her vivid imagination. I do not find that so important. In any case I found it very interesting to read. It is not for readers who are easily shocked. Banine is the pen name of Umm-El-Banine Assadoulaeff. She was born in Baku into a family of oil magnates and multimillionaires. In fact she herself was in principle a multimillionaire for a few days after the death of her grandfather, until her fortune was destroyed when Azerbaijan was invaded by the Soviet Union. In later years she lived in Paris and wrote in French. To my taste she writes very beautifully in French. I first heard of her through the diaries of Ernst Jünger. While he was an officer in the German army occupying Paris during the Second World War he got to know Banine and visited her regularly. It was not entirely unproblematic for her during the occupation when she was visited at her appartment by a German army officer in uniform. She seemed to regard this with humour. The two had a close but platonic relationship.

As I mentioned in a previous post, during the year I lived in Paris I was a frequent visitor to the library of the Centre Pompidou. One of the books I found and read there was a book by Banine about her meetings with Jünger. I believe she actually wrote three books about him and I am not sure which one it was I read. I enjoyed reading her book and it was nice to see an account of Jünger’s time in Paris which was complementary to his own. I had completely forgotten about Banine until recently. I was reminded of her by the following chain of circumstances. Together with my wife we were thinking of going on holiday to Georgia. I found an interesting organised tour visiting Georgia, Armenia and Azerbaijan. One of the places to be visited was Baku. I must confess that it was not clear to me at that point that Baku was in Azerbaijan. In any case, it occurred to me that Banine was born in Baku and I looked her up in Wikipedia. I found out that she had written the book ‘Jours caucasiens’ and I thought it might be good to read it before the planned trip. I got the book from the university library without being sure I wanted to read it. The prose of the first page captured me immediately and did not let me go. The potential trip to Georgia will not take place this year, if at all. Even if it does not it has had the pleasant consequence of leading me to rediscover Banine.

The society in which Banine grew up was the result of the discovery of oil. Her ancestors had been poor farmers who suddenly became very rich because oil-wells were built on their land. She presents her family as being very uncivilised. They were muslims but had already been strongly affected by western culture. I found an article in the magazine ‘Der Spiegel’ from 1947 where ‘Jours caucasiens’ is described by the words ‘gehören zu den skandalösesten Neuerscheinungen in Paris’ [is one of the most scandalous new publications in Paris]. It also says that her family was very unhappy about the way they were presented in the book and I can well understand that. It seems that she had a low opinion of her family and their friends and the culture they belonged to, although she herself did not seem to mind being part of it. She was attracted by Western culture and Paris was the place of her dreams. As a child she had a German governess. Her mother died when she was very young and after her father had remarried she had a French and an English teacher for those languages. She quickly fell in love with French. On the other hand, she saw having to learn English as a bit of a nuisance. Her impression was that the English had just taken the words from German and French and changed them in a strange way.

After the Russian invasion Banine’s father, who had been a government minister in the short-lived Azerbaijan Republic, was imprisoned. He was released due to the efforts of a man whose motivation for doing so was the desire to marry Banine. She was very much against this. Perhaps the strongest reason was that he had red hair. There was a superstition that red-haired people, who were not very common in that region, had evil supernatural powers. Banine’s grandmother told her a story about an alchemist who discovered the secret of red-haired people. According to him they should be treated in the following way. He cut off their head, boiled it in a pot and put the head on a pedestal. If this was done correctly then the heads would start to speak and make prophecies which were always true. Banine could not help associating her potential husband with this horrible myth. Unfortunately she was under a lot of social pressure and after hesitating a bit agreed to the marriage. Apart from being a sign of gratitude for her father’s release this was also a way of persuading her suitor to use his influence to get a visa for her father to allow him to leave Russia. In the end she accepted this arrangement instead of running away with the man she loved. At this time she was fifteen years old. Her father got the visa and left the country. Later she also got a visa and was able to leave. The last stage of her journey was with the Orient Express from Constantinople to Paris. The book ends as the train is approaching Paris and a new life is starting for her.

Stability in the multiple futile cycle

April 8, 2019

In a previous post I described the multiple futile cycle, where a protein can be phosphorylated up to n times. About ten years ago Wang and Sontag proved that with a suitable choice of parameters this system has 2k+1 steady states. Here k denotes the integral part of n/2. The question of the stability of these steady states was left open. On an intuitive level it is easy to have the picture that stable steady states and saddle points should alternate. This suggests that there should be k+1 stable states and k saddles. On the other hand it is not clear where this intuition comes from and it is very doubtful whether it is reliable in a high-dimensional dynamical system. I have thought about this issue for several years now. I had some ideas but was not able to implement them in practise. Now, together with Elisenda Feliu and Carsten Wiuf, we have written a paper where we prove that indeed there are parameters for which there exist steady states with the stability properties suggested by the intuitive picture.

How can information about the relative stability of steady states be obtained by analytical calculations? For this it is good if the steady states are close together so that their stability can be investigated by local calculations. One way they can be guaranteed to be close together is if they all originate in a single bifurcation as a parameter is varied. This is the first thing we arranged in our proof. The next observation is that the intuition I have been talking about is based on thinking in one dimension. In a one-dimensional dynamical system alternating stability of steady states does happen, provided degenerate situations are avoided. Thus it is helpful if the centre manifold at the bifurcation is one-dimensional. This is the second thing we arranged in our proof. To get the particular kind of alternating stability mentioned above we also need the condition that the flow is contracting towards the centre manifold. I had previously solved the case n=2 of this problem with Juliette Hell but we had no success in extending it to larger values of n. The calculations became unmanageable. One advantage of the case n=2 is that the bifurcation there was a cusp and certain calculations are done in great generality in textbooks. These are based on the presence of a one-dimensional centre manifold but it turns out to be more efficient for our specific problem to make this explicit.

The general structure of the proof is that we first reduce the multiple futile cycle, which has mass action kinetics, to a Michaelis-Menten system which is much smaller. This reduction is well-behaved in the sense of geometric singular perturbation theory (GSPT), since the eigenvalues of a certain matrix are negative. With this in place steady states can be lifted from the Michaelis-Menten system to the full system while preserving their stability properties. The bifurcation arguments mentioned above are then applied to the Michaelis-Menten system.

The end result of the ideas discussed so far is that the original analytical problem is reduced to three algebraic problems. The first is the statement about the eigenvalues required for the application of GSPT. This was obtained for the case n=2 in my work with Juliette but we had no idea how to extend it to higher values of n. The second is to analyse the eigenvalues of the linearization of the system about the bifurcation point. What we want is that two eigenvalues are zero and that all others have negative real parts. (One zero eigenvalue arises because there is a conservation law while the second corresponds to the one-dimensional centre manifold.) There are many parameters which can be varied when choosing the bifurcation point and a key observation is that this choice can be made in such a way that the linearization is a symmetric matrix, which is very convenient for studying eigenvalues. The third problem is to determine the leading order coefficient which determines the stability of the bifurcation point within the centre manifold.

I started to do parts of the algebra and I would describe it as being like entering a jungle with a machete. I was able to find a direction to proceed and show that some progress could be made but I very soon got stuck. Fortunately my coauthors came and built a reliable road to the final goal.