Cancer and game theory: what do they have in common? At the first sight, nothing. But going through this article you might find out that there could actually be a strong connection between these two seemingly unrelated topics.

The neoplastic process, which consists in the transformation of a normal cell into a cancer cell, starts with the accumulation of mutations leading the cell to acquire new characteristics. For instance, it is already well established that cancer cells are able to divide faster, to prevent apoptosis, and in some cases they are able to cause the formation of secondary metastatic tumors by migrating in different tissues.
In addition, cancer cells stimulate the formation of new blood vessels in the area of the tumor. This allows them to receive nutrients directly from the main source. Moreover, their impaired metabolism makes them hungry all the time and therefore they need to uptake more nutrients (i.e. amino acids) compared to normal cells.

Jumping to the other side of our dissertation, game theory is the mathematical study of the interaction between individual decision-makers. It has big implications in economics, as demonstrated by the 1994 Nobel Prize John Nash with his work on the Nash equilibrium and game theory. A good example to illustrate what game theory entails is the so called “Prisoner’s dilemma”, which can be applied in several different real situations. In this dilemma, a prisoner A and a prisoner B are asked to cooperate with the police for a crime they may have committed. If they both remain silent, they will have to stay in in prison for one year. If they both choose to cooperate with the police by betraying each other, they will each spend two years in prison. The third and last possibility is that only one of the two prisoners is a betrayer; let’s say that A betrays B. In this case A does not go to the jail, whereas B is imprisoned for three years.

In order to understand the problem on a deeper level I recapitulate the prisoner’s dilemma in Figure 1, inspired by this video.
Basically, by remaining silent they will spend the lowest (combined) number of years in prison: two years. Cooperation between the two prisoners is therefore the best joint option, but this is something that rarely occurs when the decision-makers are humans or companies.

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Figure 1 – The Prisoner’s dilemma

In the physiological context cells are able to perfectly cooperate according to their predetermined genetic fate. Instead, in the context of a tumor, cancer cells need to uptake an insane amount of nutrients to maintain their hungry and consuming metabolism.
Even though our organismal machinery is not perfect, the social interactions among our cells are closed to be perfect. Basically we could say that, within the same tissue, cells cooperate by up-taking the same amount of nutrients or, alternatively, that they share the nutrients depending on their different needs. To use the terms of the game theory, cells are usually co-operators and not betrayers. On the other hand, when cancer cells are facing normal cells in a tissue, the situation resembles the one depicted in the prisoner’s dilemma.

In the last decades a new important topic emerged in cancer research: it was indeed discovered that cells are constantly competing for nutrients, both in physiological and altered contexts. Nevertheless, the importance of this process, which is called cell competition, emerges drastically when a tumor is growing. It is now widely accepted that cancer cells are able to inhibit the growth of surrounding normal cells by several different molecular mechanisms, even at high distances. Cachexia, for instance, is a syndrome of body weight loss and anorexia that can be caused by cancer, and one part of the molecular mechanism was recently elucidated. In addition, cancer cells are able to induce apoptosis, the programmed cell death, in the surrounding cells. This intriguing process can be modelled by using the prisoner’s dilemma, although it is clearly a simplification of the real situation:

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Table 1 – Prisoner’s dilemma and cell competition. The reported numbers are used as examples. They are not necessarily representing the real situation. In this example, 100 is the total number of nutrients at disposal. The numbers refer to the final number of up-taken nutrients. 10[K] is a fixed constant surplus value of nutrients that are consumed by cancer cells when compared to normal cells.

As depicted in the table, where the total amount of nutrients is set to 100 as a reference value, cooperation between normal cells leads to both cells sharing 50% of the nutrients. Instead, at the interface between a cancer cell and a normal cell, the “stealing skills” of the malignant cell cause a decrease in the uptake of nutrients for the normal cell: only 25%. The rest is taken by the cancer cell (75%), but a part of them (represented by K=10%) is consumed by their different metabolism. Therefore the net amount of up-taken nutrients is reduced to 65%. In the last case, two cancer cells are competing for nutrients. This situation, which occurs in tumors, should in theory lead to a natural disappearance of cancer cells due to the lower efficiency in uptake; this however does not occur. Why? This is because a tumor is composed by a heterogeneous population of cells, which have different accumulated mutations. As a consequence, they constitute a society of stealers, where the hierarchy allows them to grow and divide at the expenses of the normal tissues and, in the end, of the organism.

Future studies on cell competition could therefore reveal, in the next years, that the social interactions between humans and companies are very similar to what we observe at the cellular level. This might have an important impact on cancer research and in the development of new pharmaceutical strategies to fight cancer.

 

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