Boundaries and evolutionary dynamics in cancer
Evolutionary Game Theory (EGT) is an incredibly useful mathematical tool in which to frame how the interactions between different cell types shapes selection and thus the evolutionary dynamics in cancer. One of the virtues of EGT is its simplicity. This makes it possible to approach complex problems in a qualitative manner without having to make too many assumptions. The drawback is that some times we need to dive in into a specific area of the problem in a way that conventional EGT does not make easy. One such area is space. Space is known to play a role in many key aspects of cancer but conventional EGT treats it only implicitly.
Many people have tried to understand the role of space in various types of games, mainly by letting the players play in a grid. Although a sufficiently adequate solution for many interesting questions, those models are often too complex to be studied analytically. A different approach is to use something like the Ohtsuki-Nowak transform. This would not mean that we can model space explicitly but at least we would have a first-order approximation to it.
Today, the paper that Artem Kaznatcheev, Jacob G. Scott and yours truly started a couple of years ago, is now online at the Royal Society Interface journal [link]. In it we use the ON transform to study how the evolutionary dynamics change when, during tumour growth, tumour cells reach a hard edge like the bone and, in that way, change the number of neighbours with which they will interact in their game.