## Spatializing the Go-vs-Grow game with the Ohtsuki-Nowak transform

Recently, I’ve been thinking a lot about small projects to get students started with evolutionary game theory. One idea that came to mind is to look at games that have been analyzed in the inviscid regime then ‘spatialize’ them and reanalyze them. This is usually not difficult to do and provides some motivation to solving for and making sense of the dynamic regimes of a game. And it is not always pointless, for example, our edge effects paper (Kaznatcheev et al, 2015) is mostly just a spatialization of Basanta et al.’s (2008a) Go-vs-Grow game together with some discussion.

Technically, TheEGG together with that paper have everything that one would need to learn this spatializing technique. However, I realized that my earlier posts on spatializing with the Ohtsuki-Nowak transform might a bit too abstract and the paper a bit too terse for a student who just started with EGT. As such, in this post, I want to go more slowly through a concrete example of spatializing an evolutionary game. Hopefully, it will be useful to students. If you are a beginner to EGT that is reading this post, and something doesn’t make sense then please ask for clarification in the comments.

I’ll use the Go-vs-Grow game as the example. I will focus on the mathematics, and if you want to read about the biological or oncological significance then I encourage you to read Kaznatcheev et al. (2015) in full.

## Cataloging a year of blogging: complexity in evolution, general models, and philosophy

Last month, with just hours to spare in January, I shared a linkdex of the 14 cancer-related posts from TheEGG in 2016. Now, as February runs out, it’s time to reflect on the 15 non cancer-specific posts from last year. Although, as we’ll see, some of them are still related to mathematical oncology. With a nice number like 15, I feel that I am obliged to divide them into three categories of five articles each. Which does make for a stretch in narrowing down themes.

The three themes were: (1) complexity, supply driven evolution, and abiogenesis, (2) general models and their features, (3) algorithmic philosophy and the social good.

And yes, two months have passed and all I’ve posted to the blog are two 2016-in-review posts. Even those were rushed and misshapen. But I promise there is more and better coming; hopefully with a regular schedule.

## Cataloging a year of cancer blogging: double goods, measuring games & resistance

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.

## Antoni Gaudi and learning algorithms from Nature

Happy holidays.

A few days ago, I was exploring Barcelona. This means that I saw a lot of architecture by Antoni Gaudi. His works have a very distinct style; their fluid lines, bright colours, myriad materials, and interface of design and function make for very naturesque buildings. They are unique and stand in sharp contrast to the other — often Gothic revival and Catalan Modernisme — architecture around them. The contrast is conscious; when starting out, Gaudi learned the patterns of the neo-Gothic architecture then in vogue and later commented on it:

Gothic art is imperfect, only half resolved; it is a style created by the compasses, a formulaic industrial repetition. Its stability depends on constant propping up by the buttresses: it is a defective body held up on crutches. … The proof that Gothic works are of deficient plasticity is that they produce their greatest emotional effect when they are mutilated, covered in ivy and lit by the moon.

His buildings, however, do not need to be overgrown by ivy, for Gaudi already incorporates nature in their design. I felt this connection most viscerally when touring the attic of Casa Mila. The building was commissioned as an apartment for local bourgeois to live comfortably on the ground floor off the rents they collected from the upper floors. And although some of the building is still inhabited by businesses and private residence, large parts of it have been converted into a museum. The most famous part among tourists is probably the uneven organic roof with its intricate smoke stacks, ventilation shafts, and archways for framing other prominent parts of Barcelona.

This uneven roof is supported by an attic that houses an exhibit on Gaudi’s method. Here, I could see Gaudi’s inspiration. On display was a snake’s skeleton and around me were the uneven arches of the attic — the similarity was palpable (see below). The questions for me were: was Gaudi inspired by nature or did he learn from it? Is there even much of a difference between ‘inspired’ and ‘learned’? And can this inform thought on the correspondence between nature and algorithms more generally?

I spend a lot of time writing about how we can use algorithmic thinking to understand aspects of biology. It is much less common for me to write about how we can use biology or nature to understand and inspire algorithms. In fact, I feel surprisingly strong skepticism towards the whole field of natural algorithms, even when I do write about it. I suspect that this stems from my belief that we cannot learn algorithms from nature. A belief that was shaken, but not overturned, when I saw the snake’s skeleton in Gaudi’s attic. In this post, I will try to substantiate the statement that we cannot learn algorithms from nature. My hope is that someone, or maybe just the act of writing, will convince me otherwise. I’ll sketch my own position on algorithms & nature, and strip the opposing we-learn-algorithms-from-nature position of some of its authority by pulling on a historic thread that traces this belief from Plato through Galileo to now. I’ll close with a discussion of some practical consequences of this metaphysical disagreement and try to make sense of Gaudi’s work from my perspective.

## Fusion and sex in protocells & the start of evolution

In 1864, five years after reading Darwin’s On the Origin of Species, Pyotr Kropotkin — the anarchist prince of mutual aid — was leading a geographic survey expedition aboard a dog-sleigh — a distinctly Siberian variant of the HMS Beagle. In the harsh Manchurian climate, Kropotkin did not see competition ‘red in tooth and claw’, but a flourishing of cooperation as animals banded together to survive their environment. From this, he built a theory of mutual aid as a driving factor of evolution. Among his countless observations, he noted that no matter how selfish an animal was, it still had to come together with others of its species, at least to reproduce. In this, he saw both sex and cooperation as primary evolutionary forces.

Now, Martin A. Nowak has taken up the challenge of putting cooperation as a central driver of evolution. With his colleagues, he has tracked the problem from myriad angles, and it is not surprising that recently he has turned to sex. In a paper released at the start of this month, Sam Sinai, Jason Olejarz, Iulia A. Neagu, & Nowak (2016) argue that sex is primary. We need sex just to kick start the evolution of a primordial cell.

In this post, I want to sketch Sinai et al.’s (2016) main argument, discuss prior work on the primacy of sex, a similar model by Wilf & Ewens, the puzzle over emergence of higher levels of organization, and the difference between the protocell fusion studied by Sinai et al. (2016) and sex as it is normally understood. My goal is to introduce this fascinating new field that Sinai et al. (2016) are opening to you, dear reader; to provide them with some feedback on their preprint; and, to sketch some preliminary ideas for future extensions of their work.

## Chemical games and the origin of life from prebiotic RNA

From bacteria to vertebrates, life — as we know it today — relies on complex molecular interactions, the intricacies of which science has not fully untangled. But for all its complexity, life always requires two essential abilities. Organisms need to preserve their genetic information and reproduce.

In our own cells, these tasks are assigned to specialized molecules. DNA, of course, is the memory store. The information it encodes is expressed into proteins via messenger RNAs.Transcription (the synthesis of mRNAs from DNA) and translation (the synthesis of proteins from mRNAs) are catalyzed by polymerases necessary to speed up the chemical reactions.

It is unlikely that life started that way, with such a refined division of labor. A popular theory for the origin of life, known as the RNA world, posits that life emerged from just one type of molecule: RNAs. Because RNA is made up of base-complementary nucleotides, it can be used as a template for its own reproduction, just like DNA. Since the 1980s, we also know that RNA can act as a self-catalyst. These two superpowers – information storage and self-catalysis – make it a good candidate for the title of the first spark of life on earth.

The RNA-world theory has yet to meet with empirical evidence, but laboratory experiments have shown that self-preserving and self-reproducing RNA systems can be created in vitro. Little is known, however, about the dynamics that governed pre- and early life. In a recent paper, Yeates et al. (2016) attempt to shed light on this problem by (1) examining how small sets of different RNA sequences can compete for survival and reproduction in the lab and (2) offering a game-theoretical interpretation of the results.

## Three mechanisms of dark selection for ruxolitinib resistance

Last week I returned from the 6th annual IMO Workshop at the Moffitt Cancer Center in Tampa, Florida. As I’ve sketched in an earlier post, my team worked on understanding ruxolitinib resistance in chronic myelomonocytic leukemia (CMML). We developed a suite of integrated multi-scale models for uncovering how resistance arises in CMML with no apparent strong selective pressures, no changes in tumour burden, and no genetic changes in the clonal architecture of the tumour. On the morning of Friday, November 11th, we were the final group of five to present. Eric Padron shared the clinical background, Andriy Marusyk set up our paradox of resistance, and I sketched six of our mathematical models, the experiments they define, and how we plan to go forward with the \$50k pilot grant that was the prize of this competition.

You can look through our whole slide deck. But in this post, I will concentrate on the four models that make up the core of our approach. Three models at the level of cells corresponding to different mechanisms of dark selection, and a model at the level of receptors to justify them. The goal is to show that these models lead to qualitatively different dynamics that are sufficiently different that the models could be distinguished between by experiments with realistic levels of noise.

## Dark selection and ruxolitinib resistance in myeloid neoplasms

I am weathering the US election in Tampa, Florida. For this week, I am back at the Moffitt Cancer Center to participate in the 6th annual IMO Workshop. The 2016 theme is one of the biggest challenges to current cancer treatment: therapy resistance. All five teams participating this year are comfortable with the evolutionary view of cancer as a highly heterogeneous disease. And up to four of the teams are ready to embrace and refine a classic model of resistance. The classic model that supposes that:

• treatment changes the selective pressure on the treatment-naive tumour.
• This shifting pressure creates a proliferative or survival difference between sensitive cancer cells and either an existing or de novo mutant.
• The resistant cells then outcompete the sensitive cells and — if further interventions (like drug holidays or new drugs or dosage changes) are not pursued — take over the tumour: returning it to a state dangerous to the patient.

Clinically this process of response and relapse is usually characterised by a (usually rapid) decrease in tumour burden, a transient period of low tumour burden, and finally a quick return of the disease.

But what if your cancer isn’t very heterogeneous? What if there is no proliferative or survival differences introduced by therapy among the tumour cells? And what if you don’t see the U curve of tumour burden? But resistance still emerges. This year, that is the paradox facing team orange as we look at chronic myelomonocytic leukemia (CMML) and other myeloid neoplasms.

CMML is a leukemia that usually occurs in the elderly and is the most frequent myeloproliferative neoplasm (Vardiman et al., 2009). It has a median survival of 30 months, with death coming from progression to AML in 1/3rd of cases and cytopenias in the others. In 2011, the dual JAK1/JAK2 inhibitor ruxolitinib was approved for treatment of the related cancer of myelofibrosis based on its ability to releave the symptoms of the disease. Recently, it has also started to see use for CMML.

When treating these cancers with ruxolitinib, Eric Padron — our clinical leader alongside David Basanta and Andriy Marusyk — sees the drastic reduction and then relapse in symptoms (most notably fatigue and spleen size) but none of the microdynamical signs of the classic model of resistance. We see the global properties of resistance, but not the evidence of selection. To make sense of this, our team has to illuminate the mechanism of an undetected — dark — selection. Once we classify this microdynamical mechanism, we can hope to refine existing therapies or design new therapies to adapt to it.

## Don’t take Pokemon Go for dead: a model of product growth

In the last month, some people wrote about the decay in active users for Pokemon Go after its first month, in a tone that presents the game as likely a mere fad – with article on 538, cinemablend and Bloomberg, for example. “Have you deleted Pokémon Go yet?” was even trending on Twitter. Although it is of course certainly possible that this ends up being an accurate description for the game, I posit that such conclusions are rushed. To do so, I examine some systemic reasons that would make the Pokemon Go numbers for August be inevitably lower than those for July, without necessarily implying that the game is doomed to dwindle into irrelevance.

Students in Waterloo playing Pokemon Go. Photo courtesy of Maylin Cui.

Others have made similar points before – see this article and the end of this one for example. However, in the spirit of TheEGG, and unlike what most of the press articles can afford to do, we’ll bring some mathematical modeling into our arguments.