Ratcheting and the Gillespie algorithm for dark selection

In Artem’s previous post about the IMO workshop he suggests that “[s]ince we are forced to move from the genetic to the epigenetic level of description, it becomes important to suggest a plausible mechanism for heritable epigenetic effects. We need to find a stochastic ratcheted phenotypic switch among the pathways of the CMML cells.” Here I’ll go into more detail about modeling this ratcheting and how to go about identifying the mechanism. We can think of this as a potential implementation of the TYK bypass in the JAK-STAT pathway described experimentally by Koppikar et al. (2012). However, I won’t go into the specifics of exact molecules, keeping to the abstract essence.

After David Robert Grime’s post on oxygen use, this is the third entry in our series on dark selection in chronic myelomonocytic leukemia (CMML). We have posted a preprint (Kaznatcheev et al., 2017) on our project to BioRxiv and section 3.1 therein follows this post closely.

Cancer metabolism and voluntary public goods games

When I first came to Tampa to do my Masters^[1], my focus turned to explanations of the Warburg effect — especially a recent paper by Archetti (2014) — and the acid-mediated tumor invasion hypothesis (Gatenby, 1995; Basanta et al., 2008). In the course of our discussions about Archetti (2013,2014), Artem proposed the idea of combining two public goods, such as acid and growth factors. In an earlier post, Artem described the model that came out of these discussions. This model uses two “anti-correlated” public goods in tumors: oxygen (from vasculature) and acid (from glycolytic metabolism).

The dynamics of our model has some interesting properties such as an internal equilibrium and (as we showed later) cycles. When I saw these cycles I started to think about “games” with similar dynamics to see if they held any insights. One such model was Hauert et al.’s (2002) voluntary public goods game.^[2] As I looked closer at our model and their model I realized that the properties and logic of these two models are much more similar than we initially thought. In this post, I will briefly explain Hauert et al.’s (2002) model and then discuss its potential application to cancer, and to our model.