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.

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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.

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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.

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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).

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Oxygen fueling dark selection in the bone marrow

While November 2016 might be remembered for the inauspicious political upset likely to leave future historians as confused as we are, a more positive event transpired in tandem – the 6th Integrated Mathematical Oncology (IMO) Workshop. I was honoured to take part as a member of Team Orange, where we were tasked with investigating the emergence of treatment resistance in chronic myelomonocytic leukemia (CMML).

Unlike many other cancers where the evolution of resistance to treatment is well understood, CMML is something of an enigma as the efficacy of treatment flounders even though the standard treatment doesn’t directly impinge upon tumour cells themselves.  This raises a whole host of questions, and Artem has already eloquently laid out both why this question captivated us, and the combined approach we took to probing it. In this blog post, I’ll focus on exploring one of our mechanistic hypotheses – the potential role of oxygen in treatment resistance.

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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.
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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.

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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.

imo2016_participants

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.
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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.

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Drug holidays and losing resistance with replicator dynamics

A couple of weeks ago, before we all left Tampa, Pranav Warman, David Basanta and I frantically worked on refinements of our model of prostate cancer in the bone. One of the things that David and Pranav hoped to see from the model was conditions under which adaptive therapy (or just treatment interrupted with non-treatment holidays) performs better than solid blocks of treatment. As we struggled to find parameters that might achieve this result, my frustration drove me to embrace the advice of George Pólya: “If you can’t solve a problem, then there is an easier problem you can solve: find it.”

IMO6 LogoIn this case, I opted to remove all mentions of the bone and cancer. Instead, I asked a simpler but more abstract question: what qualitative features must a minimal model of the evolution of resistance have in order for drug holidays to be superior to a single treatment block? In this post, I want to set up this question precisely, show why drug holidays are difficult in evolutionary models, and propose a feature that makes drug holidays viable. If you find this topic exciting then you should consider registering for the 6th annual Integrated Mathematical Oncology workshop at the Moffitt Cancer Center.[1] This year’s theme is drug resistance.
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