Explaining cancer dynamics with game theory

 Building a tumour takes teamwork!

Isolated groups of few cancer cells generally do not give rise to new tumours. Micrometastases, i.e. very small clusters of tumour cells, can frequently be found in the lymph nodes and bone marrow of cancer patients. These micrometastases tend to lie dormant after removal of the primary tumour – often for the remainder of the patient’s life. Moreover, it is well known that much cancer surgery leads to a veritable spraying of cancer cells in the operation wound, but it is very rare that these cells form any metastases where they land.

It is only a few years since the mainstream view of cancer researchers turned towards viewing the tumour as a complex society of cells, including tumour cells of heterogeneous natures, supporting stromal cells, and ingrowing blood vessels. These cells all have to work together in order for the tumour to grow and progress. It is a hotly debated issue whether the stromal and vascular cells are deceitfully co-opted by tumour cells which secrete growth factors similar to those occurring e.g. in wound healing, or whether the non-cancer cells surrounding the cancer cells are in themselves supporting and accelerating the tumour growth and progression.

It is in this complex tissue interplay that the tumour cells live and evolve. Cancer cells are genetically dissimilar from the people that are their hosts and progenitors, because they accumulate genetic changes of various kinds – mutations, deletions, amplifications, translocations – that enable them to proliferate independently and so on. One common first step in carcinogenesis is a genetic destabilisation, which leads to a much increased rate of genetic change. Hence, tumour cells constantly develop new genotypes and phenotypes and grow into a heterogeneous society of cells.

Now, in almost every situation where cooperation exists, dynamics come into play that are described by game theory. If everyone cooperates, it is typically advantageous for a single organism or cell to defect and reap the rewards of everyone else’s cooperativity while not contributing. This incentive to defect can lead to the collapse of the cooperative system, or to the emergence of a counter-strategy which rewards cooperators and punishes defectors. Against these strategies, in turn, there are other counter-strategies, and so the play of Nature continues. We can observe it in populations of bacteria, honey bees, wolves, and humans. And in cancer, or so we expect.

But what does it mean for a cancer cell to defect, and cease to cooperate? For about ten years, scattered groups of scientists have been building models where tumour cells of two different kinds derive certain benefits and drawbacks from being next to other cells of the same or of the other kind. (See this paper for a review.) Models like these are great fun, and they highlight the importance of evolutionary dynamics within the tumour. But thus far, the fitness modifiers have been very arbitrarily chosen, and can hardly be said to represent the physical realities of the tumour except on a very abstract level.

There are two conceptual problems that make it very difficult to conceive of what defection in a tumour cell would look like. The first is that the cancer cell bathes in the same soup of growth factors as its immediate neighbours, and many of the stimulatory signals that are emitted by the cancer cell end up targeting the cell itself – so-called autocrine stimulation. This means that if the cancer cell were to stop stimulating its neighbours, it would also stop stimulating itself, and that would hardly ever result in any fitness increase. The second problem is that the cost of signalling is very low, and most of the cooperative behaviour takes the form of signalling through secreted molecules. That means that even if another cell has something to lose if the first cell stops its signalling, the first cell has almost nothing to gain. (Anti-proliferative signalling by tumour cells is very uncommon. I do not know of any proven example.)

In a recent paper, D. Basanta and co-workers suggest a biochemical basis for an act of defection, coupled to game-theoretical interactions. Their model brings in the Warburg effect, which is common to tumours of nearly all kinds. It consists in a shift from aerobic to anaerobic metabolism – great for when the blood supply is strained, as it usually becomes when tumours grow beyond a few millimetres in size. According to their reasoning, cells that shift their metabolism in this way adversely affect their neighbours, because they release toxic metabolites. They proceed to construct a set of conditions under which invasive tumour cells start to migrate out from the tumour after sufficiently many cells have turned anaerobic. In fact, they provide a completely new theoretical framework that may explain in evolutionary terms why the Warburg effect is so ubiquitous.

As good theory should, this model yields predictions that are testable in principle. Unfortunately, it is not really possible to eliminate locally the toxic by-products of anaerobic metabolism, or to prevent the Warburg effect from appearing at all. While we wait for experimental science to catch up, these theoretical models continue to help us form a tentative understanding of the principles behind the tissue interactions in tumours.

Update: The Carnival of Evolution has just been published in its ninth edition at Moneduloides, and this post has been included!