Cataloging a year of cancer blogging: double goods, measuring games & resistance
January 31, 2017 1 Comment
Happy year of the Rooster and 2017,
This month marks the start of the 7th calendar year of updates on TheEGG. Time to celebrate and summarize the posts of the year past. In 2016 there was the same number of posts as 2015, but instead of being clustered in a period of <7 months, they were more uniformly distributed across the calendar. Every month had at least one new post, although not necessarily written by me (in the case of the single post by Abel Molina in October). There were 29 entries, one linkdex cataloging 2015, and two updates on EGT reading group 51 – 55 & 56 – 60.
In September, as part of my relocation from Tampa to Oxford, I attended the 4th Heidelberg Laureate Forum. I wrote two pieces for their blog: Alan Turing and science through the algorithmic lens and a spotlight on Jan Poleszczuk: from HLF2013 to mathematical oncology. You can read those (and more posts coming this year) on their blog. I won’t go into more detail here.
As before, this post is meant to serve as an organizing reference and a way to uncover common themes on TheEGG. A list of TL;DRs from 2016. The year was split up into four major categories: cancer, complexity & evolution, other models, and philosophy. The cancer posts make up almost half the articles from last year, and are further subdivided into three subsections: double goods game, experimental game theory, and therapy resistance. I want to focus on these cancer posts for this linkdex, and the other three categories in the next installment.
For much of the last two and a half years, I was a research associate at the H. Lee Moffitt Cancer Center & Research Institute, so it isn’t surprising that the largest contingent of articles on TheEGG were about mathematical oncology:
I opened the year with a review of three books on cancer that I read in 2015: Mukherjee, S. (2010) The Emperor of All Maladies: A Biography of Cancer, Leaf, C. (2014) The Truth in Small Doses: Why We’re Losing the War on Cancer — and How to Win It, and Nelson, S. (2013) Anarchy in the Organism (Cancer as a Complex System). I was most impressed with Leaf’s book and happy that he introduced me to the work of Judah Folkman & Mina Bissell (footnote  in the post) and the difficulties of the cancer funding system.
This post was around 3.7 thousand words long and was viewed only 212 times last year
The two projects I concentrated on the most during the first half of the year were finishing the double goods game with Robert Vander Velde, Jacob Scott, and David Basanta; and starting a project on experimentally measuring games in cancer. I presented both on July 14th at the annual meeting of the ECMB and SMB.
Double goods game
The double goods project started in late 2014 with Robert and David’s excitement about the Archetti (2013,2014) model of non-linear public goods. It saw two posts in 2014, and three more in 2015. Continuing strong last year:
- Don’t treat the player, treat the game: buffer therapy and bevacizumab (March 26th)
- Cancer metabolism and voluntary public goods games by (April 14th) Robert Vander Velde
- Acidity and vascularization as linear goods in cancer (May 16th)
- Hamiltonian systems and closed orbits in replicator dynamics of cancer (June 24th)
- Evolutionary dynamics of acid and VEGF production in tumours (July 14th)
This project has since become a pre-print (Kaznatcheev et al., 2016) that will appear shortly in the British Journal of Cancer. Although 2015 included a classification of pairwise non-linear games and a sketch of transitioning from general linear to non-linear double goods, the BJC paper is focused on the linear case. The best summary of this project so far is the July 14th post: it includes a linkdex to all the other entries. When the final paper is out, I might put out one more post to summarize the results and sketch future directions. Maybe I will follow some of these paths myself, and if you’d like to work on something related to the double goods game then get in touch with me in the comments or by email.
These 5 posts had a corpus of around 8.8 thousand words and garnered around 1.3 thousand views last year.
Experimental game theory
Together with colleagues, Archetti et al. (2015) continued his work on public goods by measuring the good used in an experimental cancer system. This encouraged me to continue thinking more about methods for operationalizing replicator dynamics, spatial structure, and measuring games:
- Measuring games in the Petri dish (January 27th)
- Lotka-Volterra, replicator dynamics, and stag hunting bacteria (February 9th)
- Choosing units of size for populations of cells (April 11th)
- Counting cancer cells with computer vision for time-lapse microscopy (April 21st)
- Population dynamics from time-lapse microscopy (May 7th)
Adopting the terminology of ‘gain functions’ from Peña et al (2014; work introduced to me by Jorge Peña in the blog comments), I focused on directly measuring gain functions as a way to characterize dynamics. Of particular interest to me was getting error bars on our estimate of the game, which means propagating errors through to the gain function. In the above post, I do that for Archetti et al. (2015) and show how errors can be amplified.
In the comments, Arne Traulsen pointed me to related work that was carried out in his lab by Li et al. (2015). Another serendipitous encounter on the blog (and why I recommend everyone to blog their work).
This resulted in a detailed set of comments from me on Li et al. (2015). In particular, I try to show how their dynamics are interpretable through the (factored) replicator equation.
Li et al. (2015) was a very important paper for me, and has greatly influenced how I thought about measuring the games that cancer plays later in the year. Although they don’t explicitly measure a game or propagate errors (see footnote 10 of the above post), I think their method of taking their estimate of fitness from the growth phase (i.e. implicitly assuming approximation by an exponential growth model; which is fine, see my June 9th post on multiple realizability of replicator dynamics) is a better approach than my original plan of focusing exclusively on the gain function.
To just reach the point of even estimating the growth rates in a cancer system, however, required all of the above three posts. Along the way, I got to really appreciate the power of Python and play with some simple computer vision. However, that is just the first step in the pipeline, and the least interesting for me in the long term. This means that there is a lot of room for refinement in my image processing, and if you’re a computer science student interested in cancer and computer vision then get in touch with me in the comments or by email. There are some fun and very useful extensions here.
We are currently preparing a preprint on this work. Expect to see more technical posts on the topic as I flesh out the supplementary materials. Hopefully, I will have the energy to write posts on the games that we actually measured in the next few months.
These 5 posts had a corpus of around 11.8 thousand words and garnered around 3.1 thousand views last year.
Although I moved from Tampa to Oxford towards the end of this year, I couldn’t stay away for long and returned for the 6th annual IMO Workshop. The year’s theme was resistance. So I warmed up with a post that examined the conditions under which drug holidays could theoretically help control a tumour population:
- Drug holidays and losing resistance with replicator dynamics (September 2nd)
- Dark selection and ruxolitinib resistance in myeloid neoplasms (November 9th)
- Three mechanisms of dark selection for ruxolitinib resistance (November 25th)
The above post focuses on a classic Darwinian model for the evolution of resistance. I show that if these classical dynamics are described by logistic growth then drug holidays cannot help, and need to be supported by effects like phenotypic switching. Writing that post had put me in a mindset of thinking outside the Darwinian box.
During the workshop, I got a chance to really step out of the box. We were faced with a case of resistance that didn’t seem to be following the classic picture of an exponentially shrinking population followed by relapse due to the clonal growth of an initially rare resistant population. There was no clear source of selection. So we had to consider other mechanisms of resistance as a way to find this dark selection.
During my week in Tampa, we were able to come up with three mechanisms for resistance and a way to select between them based on the sort of experimental data we might hope to have from a mouse model (and maybe someday patients). The judges liked our approach, and we ended up winning the competition and securing a $50k start-up grant to continue our ideas on dark selection. So this year, you can expect more posts and a preprint on this topic. In fact, David Robert Grimes already has a draft post ready on the role of oxygen in dark selection, tying together some themes from my various cancer focuses in 2016.
These 3 posts had a corpus of around 5.0 thousand words and garnered just 474 views last year.
Archetti, M. (2013). Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies. British Journal of Cancer, 109(4): 1056-1062.
Archetti, M. (2014). Evolutionary dynamics of the Warburg effect: glycolysis as a collective action problem among cancer cells. Journal of Theoretical Biology, 341: 1-8.
Archetti, M., Ferraro, D.A., & Christofori, G. (2015). Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer. Proceedings of the National Academy of Sciences of the USA, 112(6): 1833-8.
Kaznatcheev, A., Vander Velde, R., Scott, J. G., & Basanta, D. (2016). Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature. arXiv:1608.00985 (to appear in British Journal of Cancer, 2017).
Li, X.-Y., Pietschke, C., Fraune, S., Altrock, P.M., Bosch, T.C., & Traulsen, A. (2015). Which games are growing bacterial populations playing? Journal of the Royal Society Interface, 12(108).
Peña, J., Lehmann, L., & Nöldeke, G. (2014). Gains from switching and evolutionary stability in multi-player matrix games. Journal of Theoretical Biology, 346: 23-33.