Beyond evolution: game theory and the progression of cancer (2014)

I occasionally teach a graduate-level biological physics course, not very well at all of course but I try to teach what is not known. Although I do cover some of the classic ‘nuts and bolts’ topics of biomolecules and biological systems, in this course I deliberately try to take to heart the famous statement by Dobzhansky that ‘Nothing in Biology Makes Sense in the Light of Evolution’ (although Dobzhansky himself unfortunately was actually espousing theistic evolution). If you actually look at the several graduate-level textbooks out there on biophysics or biological physics (e.g. those by Phillips et al., Nelson, Bialek) the number of times the subject of evolution is tackled is … zero. So, apparently the most important idea in biology is not worthy of mention by biological physicists. That is a huge omission, and it shows no signs of being corrected in the near future.

Ignoring evolution in biology is a particularly bad mistake if one wants to understand cancer at a deep level, which is one of the charges that the National Cancer Institute gave the 12 Physical Sciences Oncology Centers that were founded as an experiment in 2009. Cancer, to first order, is an incurable condition, and it is incurable because of evolution: cancer cells typically evolve resistance to whatever toxic chemotherapy or treatment the patient is subjected to … a losing game generally.

Not all physicists doing biology ignore evolution. The Princeton Physical Sciences Oncology Center takes evolution very seriously, and it takes the dynamics of evolution among interacting cells seriously because we feel that understanding complex evolution amongst different phenotype cells is one of the keys to understanding cancer. More formally, evolution dynamics among interacting cells falls into the domain of a fascinating branch of science called evolutionary game theory.

The series of papers presented in this Theme Issue stem from a second-day Workshop on Game Theory held at Johns Hopkins University by the Princeton Physical Sciences Oncology Center in June 2013 to try and explore the implications of game theory in cancer progression, with an emphasis on evolutionary game theory. Unfortunately, only about one-half of the speakers responded to our call to submit papers for this issue, but fortunately the ones we did get capture I think the range of game theory ideas and their applications to cancer progression discussed at the workshop.

I believe the papers should be read in a particular order for the serious student. For a solid introduction to game theory from a broad perspective, I can highly recommend the paper by Lambert et al. [1] in spite of being a co-author. The title seems a bit bizarre, what does game theory have to do to bacteria and further, what does it have to do with cancer? But the paper starts with an elegant description of evolutionary game theory and uses the rapidly growing communities of bacteria to quickly explore some of the basic concepts.

The next two papers to be digested are the pairs of papers submitted by Liao & Tlsty [2,3]. The paper by Lambert et al. [1] really takes place in one spatial dimension, with general concepts. This pair of papers by Liao and Tlsty offers a wonderful introduction to how one can generalize the concepts to two spatial dimensions, how you can extract the relevant reward matrix elements from the data, and, in addition, provides a provocative section on the dangers in this approach to over-fitting the data, and more powerfully the dangers in making the agents in game theory sentient beings rather than variables in a set ordinary differential equations.

The next paper, by Wu et al. [4], where again my name appears at the end, is a natural extension of the Liao and Tlsty papers where the calculus of evolutionary game theory is applied to an in vitro system designed to mimic the spatial complexity of a true cancer ecology, and attempts to see how in this semi-simplified setting the deterministic solutions to evolutionary game theory can be used to extrapolate forwards in time, with some promising results.

The last two papers get down to the hard business of applying game theory to actual cancer cell populations in a clinical setting. The paper by Pacheco et al. [5] is the more complete and tutorial of the two hardcore cancer game theory papers and can be read as a companion to the paper by Liao and Tlsty for a more direct connection to the clinical implications of the more classical elements of evolutionary game theory in terms of interacting populations of cells.

The paper by Kianercy et al. [6] really is an outlier in the sense that here the game is played not so much between the players but rather between the players and the metabolic resources of the ecology, and in that sense goes beyond the normal boundaries of game theory into new territory. It is succinct to the point of leaving a lot of the math hidden to the reader, and demands the most of the reader if you want to understand it.

Taken together, I think the papers capture a great deal of what was covered at the workshop, and with a minimum of hand waving and ‘it can be shown that’ (really? Can it?) statements allow an interested physicist or well-educated biologist some real insights into where game theory can truly be applied to one of the great problems in biology, which may only make sense in the light of evolution.