On Highly Recurrent Cancer Mutations

I hit upon this insight which I thought I should share it with you. This is purely from analytical perspective.

One would wonder why in some cancers, certain residues/mutations (like R132H, V600E etc) are almost always found at high frequencies. There could be a simple game theoretical explanation to it.

In game theory, there is something called mixed and pure strategies. For instance, let us say Charlie and Ruth are playing Rock-Paper-Scissors game. Charlie/Ruth can choose to call “Rock" all the time (or for that matter either “Paper" or “Scissors" all the time). This is called pure strategy – that is, choosing a particular option all the time. On the other hand, Charlie/Ruth can alternate between rock,  paper and scissors in certain frequencies. For instance, calling rock 5/10 times, paper 2/10 times and scissors 3/10 times. This is called mixed strategy. 

There is a nice theorem that says: if Charlie “knows” what Ruth is going to play, then the optimal counter strategy for Charlie is always a pure strategy and not a mixed strategy. The same result holds for Ruth as well. This is a very interesting result because regardless of what the other person plays (could be pure or mixed with any frequency), if a player “knows” what is going to be played, the optimal play for him is to choose a pure strategy. And pure strategy is choosing one option all the time.

Therefore, applying this in a cancer setting: if a gene like IDH or BRAF somehow “senses” the frequency of other events, the optimal strategy for it would be a pure strategy or in other words, mutating at a particular residue all the time. That could just be R132H or V600E. The gene just needs to sense the pattern rather than the frequency of actual events in order to get mutating at a particular residue almost always.

I know this argument devoid of any biology does not say why that particular residue, but it could be a small rationale for why we see what we see.