The road to measuring evolutionary games in cancer

After I finished residency I actually wasn't able to negotiate for a full faculty job that had the parameters I was looking for (read: protected time, lab startup). But, I had worked for so long to get to the physician-scientist track that I wasn't willing to accept less than what I thought I needed to succeed.  This is something we can revisit in another post, but it sets the scene for this story, because what I did was take a sort of combination fellow/post-doc position where I trained. My two chairs, Sandy Anderson (Integrated Mathematical Oncology) and Lou Harrison (Radiation Oncology) were open minded and generous enough to create a position for me, so that I could get started on research that might lead me to be more competitive the next cycle.

This ended up being a super productive year, and led me to the job I now have (many thanks!). Also, during that year I met Andriy Marusyk, who is now my principle collaborator, and a close friend (sadly, not close in distance, but that's ok). Also during that year, Artem Kaznatcheev was working in Tampa with David Basanta, another friend and collaborator (and game theorist) of mine. At the time, Jeff Peacock was a 4th year medical student at UCF, and was rotating in my lab before starting his radiation oncology residency at Moffitt where I was (pseudo)faculty. During the course of that year, we had weekly discussion and brainstorming sessions, which were low stress, exciting times (Figure 0).

Figure 0. Artem, Robert and Andrew. Three awesome PhD students, discussing this project in what was likely the best office I will ever have.

David and Artem and I had been working for some time on evolutionary game theory (EGT) -- in the form of theoretical models. As a matter of fact, the first time we interacted with Artem produced a 96 hour hackathon and one of our most influential papers to date which I (and Artem) have previously blogged about -- an exploration of the effect of interaction neighborhood size on EGT dynamics (See Figure 1) - where we applied an algebraic transform on the game matrix to account for local interactions, derived from evolutionary graph theory, called the Ohtsuki-Nowak transform (more here on Artem's blog, or the original paper).

Figure 1. Taking a cartoon version of a tumor (upper left) and a prescribed (invented) evolutionary game to go with it (just below, left-most equation), we can transform the game to take into consideration the relative opportunities to interact with different types based not just on frequency, but also on location. This yields a somewhat messier game matrix (right-most equation), but also lets you explore how the dynamics will change with changing neighborhood size (lower left).

Andriy had just come off an exciting paper where he and colleagues explored an experimental model of breast cancer dynamics and showed that 'non-cell autonomous effects' (i.e. interactions) could change the overall composition of a tumor. In this paper, they used different fluorescent labels to track proportions of different types over time. This led our discussions to how we might be able to directly measure a game over time (there is a nice series of more technical blog posts by Artem which you can find referenced in the most recent in the series: here).

In addition to being ABLE to measure a game, we wanted to start with a situation which we thought would have a decent chance of also being interesting. We had just come off a project studying the changes in drug sensitivity over time of ALK mutated non-small cell lung cancer, and so had evolved TKI-resistant lung cancer cells lying around. We hypothesized (as most were at the time) that there would be a *cost* to the resistance, which we might be able to take advantage of in the form of a measurable *trade-off*. A quick and dirty first experiment that Jeff ran gave us some hope that this might be true (Figure 2).

Figure 2. We plot drug (Alectinib) dose on the x-axis, and optical density on the y-axis for three cell types, evolved Alectinib resistant H3122 (blue), drug sensitive H3122 (red) and Cancer Associated Fibroblasts (grey). We see that the higher fitness of naive cells at low drug dose switches to a lower fitness (relative to the resistant) at high dose.

We termed this result 'the cross' as our proxy for fitness (in this case optical density) *crossed* at a specific drug dose.  That is, after a specific dose, the most fit cell type changed from the wild type to the resistant, but critically, at low doses, we saw that the wild type was higher fitness than the resistant -- confirming our hypothesis (and bias) that at low drug concentration, being resistant *carried a cost* of lower growth rate. Interestingly, when we played this out in a different experimental system (measuring growth rate in a time lapse microscope), this fitness cost disappeared (see right-most two sub-figures in Figure 3).  I sometimes wonder if we would have continued with the experiment if we hadn't see this cost up front... 

Figure 3. Naive H3122 and evolved resistant to Alectinib (erAlec) cells grown in monoculture compared across four experimental conditions.

Anyways, by the time we measured the growth rates in Figure 3, Artem had already come up with a clever way to directly measure a game (which we assume to be a linear matrix game). By plating sensitive and resistant cells in a variety of proportions (ranging from 0:100 to 100:0) and measuring growth rate (proxy for fitness), then fitting a line, the intercepts would be the entries to the payoff matrix!  Figure 4 is the figure from the paper showing 4 different experimental conditions (with/without Alectinib and with/without Cancer Associated Fibroblasts (CAFs)).  It is a little busy, but it has ALL the info.  The inset plots are example shots of how we measured growth rate, by figuring out the total area of each (minor y-axis) red and green (sensitive and resistant) frequently over time (minor x-axis). Each of the individual proportion conditions are then plotted on the major axes with the opacity of the point telling what plated proportion were parental.

Figure 4. ALL THE DATA. Each experimental condition is a different color/shape as represented by the labelled convex hulls. Opacity is plating proportion of parental (1-resistant). The inset show how we obtained the growth rates, with example data points shown (green and red lines).

To explain how we get from here to a familiar appearing game notation, I'll 'blow up' one of the datasets (the Alectinib treated one - blue squares - in the far left convex hull).

Figure 5. Blowing up just the Alectinib treated cells, we can see how each data point in Figure 4 corresponds to a pair of points in the left sub-figure here (and the x/y axis in Figure 4). 

All the data points here are paired (80:20 etc), and the pairs (vertically aligned) match up to a single point in the previous figure. You can see here that we then perform a linear fit, which we can now use the intercepts to derive the payoff matrix elements, like this:

Figure 6.  We can now see how the intercepts of these lines forms the entries into the familiar payoff matrix.

Now we have a familiar payoff matrix!!  We can then plot the payoff matrix in a game space (which Artem nicely explains on his blog here), and compare the experimental conditions -- and we see that the DMSO+CAF game is qualitatively different than the others (Figure 7).  A cool result on its own. The canonical games represented are 'Leader' and 'Deadlock' - games which have not received much (any) attention to date in the oncology-EGT literature.

Figure 7 - some future directions/food for thought...

Another fun thing we noticed is that it appears that each perturbation (drug/CAF) shift the game in a particular way (see cartoon versions of vectors representing these changes in the game in red and blue). We haven't fully explored this yet, but it is thought provoking...

Taken together, we have a new assay, which we hope more folks use to measure a catalogue of games played by other cancer types, and a new way to perturb evolution -- by treating the game instead of the player. The central focus of our lab is exactly this: to get control of/take advantage of the evolutionary process on the way to resistance.  While this assay, and the resulting measured game, takes place over a short time-scale (5 days), it does give some insight into some new ways to pick/bias the winner in a low complexity game. We are hoping to extend the assay to more strategies to better represent more complex tumors, and also to think about longer timescales -- this will require not just new experimental technique, but some new theory as well. Further, this theory fits in well with the work on collateral sensitivity which we recently reported in E. coli with Dan Nichol as lead author... though that work is the opposite end of the time-scale spectrum (relatively very long time scales - actually infinite time in the theoretical work, but ten-days in the experimental work, which for bacteria is MUCH longer than the 5 days in cancer cells here).

Anyways, the work continues! For more information on measuring games, check out the full paper: 

Fibroblasts and alectinib switch the evolutionary games played by non-small cell lung cancer 

published last week in the journal Nature Ecology and Evolution, along with an associated editorial which describes a bit more about evolutionary therapy.