Math Therapy

An interview by Ivan Erofeev with Dr. Alexander Bratus about the ways in which mathematics can help in the fight against cancer and the prospects of ‘living medicines’

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An interview with Alexander Bratus

An interview by Ivan Erofeev

Alexander Bratus is a Scientific Doctor of Physics and Mathematics, a professor at the Department of System Analysis of the Faculty of Computational Mathematics and Cybernetics at Moscow State University, and a Head of the Department of Applied Mathematics at Moscow State University of Railway Engineering.

Recently, Alexander Bratus has been dealing with the use of mathematical models for solving medical and biological problems. We talked to him about how mathematics can help in the fight against cancer, and discussed the prospects for the development of 'living medicines'.
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Why have you, a mathematician, become engaged with biological problems? How have you come to this?

I was always interested in opportunities for the application of mathematical methods and models to biological problems. At first I studied the experience of other scientists in this field. Around the year 2000, I stumbled upon an article by two Italians who saw cancer as a mathematical model. I became interested in this topic and collected all the literature that was available. Afterwards I realized that there was a potential for me in this area, as my math background was richer than that of those guys. We began to produce our own models, but it appeared that we took it up quite late. By that moment there was a whole international community dealing with these problems abroad. I must say the following, although it is probably a disappointing thing. The fact is that by now I do not know any mathematical work on models of cancer therapy, which have been applied in practice. I came across some doctors who were interested in what we were doing. When we showed them our results they said they did it in quite the same way. To put the results of mathematical research into practice, it is necessary to have a group of mathematicians, biologists, physicians and a certain experimental basis providing them with data. But here it doesn’t work this way; mathematicians, biologists and physicians don’t intersect. The degree of our responsibility is also different. Doctors are responsible for the patient’s life, while mathematicians are responsible only for the results of the proposed mathematical model.


Professor Bratus with his postgraduate students helping him in cancer treatment modelling

Do such groups exist anywhere?

They do exist. There are some at the National Institute of Health in the United States. It is a huge institution, located in the suburbs of Washington. It is very well funded. In general a huge number of people are engaged with it in America, because there it is officially declared that human health is a priority. In addition, there are similar centers in Spain, France and Poland. Actually, mathematicians established their interest in this topic quite a long time ago. The first works in this direction appeared in the seventies.

Let’s talk about your current project related to cancer treatment. What’s the point of it?

Cancer is an extremely complex process: the cancer cells spread and mutate, somehow affect normal and immune cells and can induce blood vessel sprouting for additional power supply and they don’t die in conditions in which healthy cells are killed. Injected drugs affect cancer cells as well as healthy and immune ones. The drug concentration in the body is constantly changing in a nonlinear manner. The first problem for a researcher is how to create a mathematical model of the therapy process. It’s clear that such a model should be appropriate, and not too complicated, since a complex model is difficult to study. These are two conflicting requirements and it is not easy to find a compromise between these two extremes. As a model is constructed, it is necessary to state the purpose of the process. For example, to find a treatment strategy that would make it possible to destroy the maximum number of diseased cells.

Mathematical models cannot tell you if it is possible or impossible to cure a person. The purpose of these models is another – to find patterns

In a recent interview you said that the general trend now is not to cure cancer, but to fight for the person’s life so that he or she lives as long as possible with the disease. Do you consider this a global trend?

There are several points of view. Some types of cancer can be cured completely. There are great strides in the treatment of leukemia, breast cancer and many others. On the other hand, a set of diseases is incurable (melanoma, glioma, et cetera). It is impossible to say that this is a general trend. However, the goal of any treatment is either to cure completely the patient or to transfer a disease into a chronic phase, that is, in a state where it can be controlled. Many also believe that the cancer cells had the same evolutionary development as an ordinary one. It also has a great vitality stock. We live with certain diseases, so it is possible to find some balance. I don’t want to say that this is the only approach, but it is quite actively used, for example, in the treatment of diabetes and many other diseases.

I have heard from my friend who is a biologist that targeted treatment is one of the most popular fields in the cancer treatment today. ‘Targeted’ means that the drug attacks only diseased cells, destroying them or freezing, without any harm to the immune system.

This is really one of the central areas of therapy now, it’s called ‘smart drugs’. You see, I’m not a doctor, I deal with mathematical models, and quite rough ones. Mathematical models cannot tell you if it is possible or impossible to cure a person. The purpose of these models is another – to find some patterns. And then to test them. And I’m repeating, these are pretty primitive models. It would be similar situation if we regarded a human being as a ball as a first approximation. But mathematical models work very well in many areas of physics, mechanics, chemistry. Why wouldn’t they become useful in biology and medicine as well? The history of the development of mathematical biology gives us such examples.

In 1966 in America there was an experiment: they connected two computers that exchanged information. And no one could think that out of this the Internet can emerge

Besides that, do you have other projects related to biomedical topics?

In my opinion, the study of so-​called replicator systems is a very promising area. It is a system of interconnected, self-​replicating macromolecules. An example of such a system is RNA (Ribonucleic Acid – one of the three major macromolecules contained in the cells of all living organisms). Mathematical models of such systems were offered by German scientist and Nobel laureate Manfred Eigen. One of them is called a hypercycle. This model is an example of the simplest cooperation, where each macromolecule in the process of reproduction helps neighboring macromolecules within the associated cycle, so that the latter helps the first, et cetera. This model has a number of remarkable properties. For instance, it can reproduce itself. An interesting fact is that the idea of the hypercycle, which arose as a result of theoretical research, found its incarnation in reality. In 2009, a hypercycle was obtained by biochemical method, which consisted of two macromolecules, and in 2012 a six macromolecule hypercycle was realized the same way.

What practical outcome can this research lead to?

In practical terms, we can show how the systems of macromolecules and their network should be arranged, so that altogether, they would be similar to something living. For example, it will be possible to create a medicine that can reproduce itself. It can be delivered to the necessary place, where a certain environment is created which would sustain it and therefore this medicine would recreate itself and constantly function. It is still of course a fantastic project, we do not set such goals yet. We research mathematical models, but they may possibly lead to unexpected applications. If you look at the history of science, you’ll see that in 1966 in America there was an experiment: they connected two computers that exchanged information. And no one could think that out of this the Internet can emerge.

In which fields of medicine and biology are mathematical models also applicable? What is the future of the mathematical models assisting other sciences, not connected to mathematics and physics?

Mathematical models and methods are applied now in many spheres of biology and medicine. For instance, analyzing electrocardiograms and methods of shunting in complicated cases (which is studied at the Institute of Hydrodynamics in Novosibirsk). Finally, the most advanced field of biology – network analysis of the DNA nuclides sequences is called bioinformatics, and is entirely based on the use of mathematical methods. There are several international journals, devoted entirely to the use of mathematical models in medicine.

Where does science develop the most rapidly at the moment?

Primarily, in the USA, obviously. There are a lot of universities, many of them are research ones, which very much stimulate the development of science. The completion to write for scientific magazines is enormous. It is not easy to get published in an authoritative journal. There are only few serious magazines on physics and mathematics where decent articles are being published. But there are many magazines which contribute very little to international fame. Actually, in the current situation, Russian science slides to a provincial level and that is why one has to aspire to get published in international magazines, which is not easy at all. Besides, a large number of Chinese researchers have created a specific situation. The thing is, if you are an employee of a Chinese university and your article is published in an international magazine, your salary rises twice or three times. That is why Chinese scholars innundate the magazines with their articles, it is a generally known fact. China spends very large sums of money on their science, something not peculiar to our country.

Russian science slides to a provincial level and that is why one has to aspire to get published in international magazines, which is not easy at all

Have there been any significant discoveries in the field of mathematics? Is it a forerunner of the sciences at the moment or is it limited to the functions of a supporting science?

Pure mathematics does not require any stimulus from the outside and develops according to its inherent laws. However, it is rather typical that the outcome of an abstract mathematical research can be applied to solve certain practical problems. On the other hand, the emergence of the new problems within physics, chemistry and biology stimulates the development of new directions in mathematics. The modeling of biological systems resulted in profound research into the nonlinear system of differential equations, et cetera. I do not mention the probability theory, which is used everywhere from sports to astrophysics. To cut a long story short, new problems of natural sciences stimulate the development of the old and new directions in mathematics, and then mathematical apparatus becomes a tool that helps to solve various problems in various fields of science. Therefore, mathematics as an abstract science (a specific field of philosophy) develops according to its inherent laws, while other sciences use various aspects of mathematics. It is a complementary process, as the needs of the sciences stimulate the development of certain areas of mathematics, which are called applied mathematics. Significant discoveries in mathematics occur, but most of them are hardly explicable or inexplicable at all for those who are generally ignorant of mathematics. Out of the recent achievements, the proof of Fermat’s Last Theorem and the proof of the Poincare conjecture by Perelman can be noted.