The wei wu wei of evolutionary oncology

The world was disordered, rains would come and the rivers would flood. No one knew when. When it rained, plants would grow, but no one knew which were fit to eat and which were poisonous. Sickness was rife. Life was precarious.

The philosopher-king Yu dredged the rivers, cleaned them so they would flow into the sea. Only then were the people of the Middle Kingdom able to grow the five grains to obtain food.

Generations later, Bai Gui — the prime minister of Wei — boasted to Mengzi: “my management of the water is superior to that of Yu.”

Mengzi responded: “You are wrong. Yu’s method was based on the way of the water. It is why Yu used the four seas as receptacles. But you are using the neighbouring states as receptacles. When water goes contrary to its course, we call if overflowing. Overflowing means flooding water, something that a humane man detests… As for Yu moving the waters, he moved them without interference.”

Although Yu made changes to the environment by digging channels, he did so after understanding how the water flowed and moved naturally. He did so with knowledge of the Way. Yu’s management of water was superior to Bai Gui’s because Yu’s approach was in accordance with the Way. This is what evolutionary oncology seeks to achieve with cancer treatment. By understanding how the dynamics of somatic evolution drive tumour growth, we hope to change the selective pressures in accordance with this knowledge to manage or cure the disease.
Read more of this post

Advertisements

Looking for species in cancer but finding strategies and players

Sometime before 6 August 2014, David Basanta and Tamir Epstein were discussing the increasing focus of mathematical oncology on tumour heterogeneity. An obstacle for this focus is a good definitions of heterogeneity. One path around this obstacle is to take definitions from other fields like ecology — maybe species diversity. But this path is not straightforward: we usually — with some notable and interesting examples — view cancer cells as primarily asexual and the species concept is for sexual organisms. Hence, the specific question that concerned David and Tamir: is there a concept of species that applies to cancer?

I want to consider a couple of candidate answers to this question. None of these answers will be a satisfactory definition for species in cancer. But I think the exercise is useful for understanding evolutionary game theory. With the first attempt to define species, we’ll end up using the game assay to operationalize strategies. With the second attempt, we’ll use the struggle for existence to define players. Both will be sketches that I will need to completely more carefully if there is interest.

Read more of this post

QBIOX: Distinguishing mathematical from verbal models in biology

There is a network at Oxford know as QBIOX that aims to connect researchers in the quantitative biosciences. They try to foster collaborations across the university and organize symposia where people from various departments can share their quantitative approaches to biology. Yesterday was my second or third time attending, and I wanted to share a brief overview of the three talks by Philip Maini, Edward Morrissey, and Heather Harrington. In the process, we’ll get to look at slime molds, colon crypts, neural crests, and glycolysis. And see modeling approaches ranging from ODEs to hybrid automata to STAN to algebraic systems biology. All of this will be in contrast to verbal theories.

Philip Maini started the evening off — and set the theme for my post — with a direct question as the title of his talk.

Does mathematics have anything to do with biology?

Read more of this post

Symmetry breaking and non-cell-autonomous growth rates in cancer

“You can’t step in the same river twice” might seem like an old aphorism of little value, but I think it is central to making sense of the sciences. This is especially clear if we rephrase it as: “you can’t do the same experiment twice”. After all, a replication experiment takes place at a different time, sometimes a different place, maybe done by a different experimenter. Why should any of the countless rules that governed the initial experiment still hold for the replicate? But our methodology demands that we must be able to repeat experiments. We achieve by making a series of symmetry assumptions. For example: the universality or homogeneity of physical laws. We can see this with early variants of the principle of sufficient reason in Anaximander and Aristotle. It developed closer to the modern statements with Galileo, Copernicus and Newton by pushing the laws of physics outside the sublunary sphere and suggesting that the planets follows the same laws as the apple. In fact, Alfred North Whitehead considered a belief in trustworthy uniformity of physical laws to be the defining feature of western philosophy (and science) since Thales.

In this post, I want to go through some of the symmetries we assume and how to break them. And I want to discuss this at levels from grand cosmology to the petri dish. In the process, I’ll touch on the fundamental constants of physics, how men stress out mice, and how standard experimental practices in cancer biology assume a cell-autonomous process symmetry.

Read more of this post

Deadlock & Leader as deformations of Prisoner’s dilemma & Hawk-Dove games

Recently, I’ve been working on revisions for our paper on measuring the games that cancer plays. One of the concerns raised by the editor is that we don’t spend enough time introducing game theory and in particular the Deadlock and Leader games that we observed. This is in large part due to the fact that these are not the most exciting games and not much theoretic efforts have been spent on them in the past. In fact, none that I know of in mathematical oncology.

With that said, I think it is possible to relate the Deadlock and Leader games to more famous games like Prisoner’s dilemma and the Hawk-Dove games; both that I’ve discussed at length on TheEGG. Given that I am currently at the Lorentz Center in Leiden for a workshop on Understanding Cancer Through Evolutionary Game Theory (follow along on twitter via #cancerEGT), I thought it’d be a good time to give this description here. Maybe it’ll inspire some mathematical oncologists to play with these games.

Read more of this post

Cataloging a sparse year of blogging: IMO workshop and preprints

Happy 2018!

With 2017 finally behind us, TheEGG enters its 8th calendar year. This past year has been a slow one for the blog, with only 10 new articles and two posts cataloguing 2016 (on cancer and on more theoretical aspects of evolution and general modelling). Half the months were barren: I posted nothing in March, April, May, July, August, September; and only October and November saw more than one post. But those two months of activity were good. We saw the list of TheEGG authors joined by David Robert Grimes, Vincent Cannataro, and Matthew Wicker; plus the return of Robert Vander Velde.

If you’re keeping score at home, this means that I only wrote six new articles last year.

As in the past, I want to start the new year by summarizing the old.

Read more of this post

Dark selection from spatial cytokine signaling networks

Greetings, Theory, Evolution, and Games Group! It’s a pleasure to be on the other side of the keyboard today. Many thanks to Artem for the invite to write about some of our recent work and the opportunity to introduce myself via this post. I do a bit of blogging of my own over at vcannataro.com — mostly about neat science I stumble over while figuring out my way.

I’m a biologist. I study the evolutionary dynamics within somatic tissue, or, how mutations occur, compete, accumulate, and persist in our tissues, and how these dynamics manifest as aging and cancer (Cannataro et al., 2017a). I also study the evolutionary dynamics within tumors, and the evolution of resistance to targeted therapy (Cannataro et al., 2017b).

In November 2016 I attended the Integrated Mathematical Oncology Workshop on resistance, a workweek-long intensive competitive workshop where winners receive hard-earned $$ for research, and found myself placed in #teamOrange along with Artem. In my experience at said workshop (attended 2015 and 2016), things usually pan out like this: teams of a dozen or so members are assembled by the workshop organizers, insuring a healthy mix of background-education heterogeneity among groups, and then after the groups decide on a project they devise distinct but intersecting approaches to tackle the problem at hand. I bounced around a bit early on within #teamOrange contributing to our project where I could, and when the need for a spatially explicit model of cytokine diffusion and cell response came up I jumped at the opportunity to lead that endeavor. I had created spatially explicit cellular models before — such as a model of cell replacement in the intestinal crypt (Cannataro et al., 2016) — but never one that incorporated the diffusion or spread of some agent through the space. That seemed like a pretty nifty tool to add to my research kit. Fortunately, computational modeler extraordinaire David Basanta was on our team to teach me about modeling diffusion (thanks David!).

Below is a short overview of the model we devised.

Read more of this post

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.

Read more of this post

Identifying therapy targets & evolutionary potentials in ovarian cancer

For those of us attending the 7th annual Integrated Mathematical Oncology workshop (IMO7) at the Moffitt Cancer Center in Tampa, this week was a gruelling yet exciting set of four near-all-nighters. Participants were grouped into five teams and were tasked with coming up with a new model to elucidate a facet of a particular type of cancer. With $50k on the line and enthusiasm for creating evolutionary models, Team Orange (the wonderful team I had the privilege of being a part of) set out to understand something new about ovarian cancer. In this post, I will outline my perspective on the initial model we came up with over the past week.

Read more of this post

Hackathons and a brief history of mathematical oncology

It was Friday — two in the morning. And I was busy fine-tuning a model in Mathematica and editing slides for our presentation. My team and I had been running on coffee and snacks all week. Most of us had met each other for the first time on Monday, got an inkling of the problem space we’d be working on, brainstormed, and hacked together a number of equations and a few chunks of code to prototype a solution. In seven hours, we would have to submit our presentation to the judges. Fifty thousand dollars in start-up funding was on the line.

A classic hackathon, except for one key difference: my team wasn’t just the usual mathematicians, programmers, computer & physical scientists. Some of the key members were biologists and clinicians specializing in blood cancers. And we weren’t prototyping a new app. We were trying to predict the risk of relapse for patients with chronic myeloid leukemia, who had stopped receiving imatinib. This was 2013 and I was at the 3rd annual integrated mathematical oncology workshop. It was one of my first exposures to using mathematical and computational tools to study cancer; the field of mathematical oncology.

As you can tell from other posts on TheEGG, I’ve continued thinking about and working on mathematical oncology. The workshops have also continued. The 7th annual IMO workshop — focused on stroma this year — is starting right now. If you’re not in Tampa then you can follow #MoffittIMO on twitter.

Since I’m not attending in person this year, I thought I’d provide a broad overview based on an article I wrote for Oxford Computer Science’s InSPIRED Research (see pg. 20-1 of this pdf for the original) and a paper by Helen Byrne (2010).

Read more of this post