## 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?

## Abstract is not the opposite of empirical: case of the game assay

Last week, Jacob Scott was at a meeting to celebrate the establishment of the Center for Evolutionary Therapy at Moffitt, and he presented our work on measuring the effective games that non-small cell lung cancer plays (see this preprint for the latest draft). From the audience, David Basanta summarized it in a tweet as “trying to make our game theory models less abstract”. But I actually saw our work as doing the opposite (and so quickly disagreed).

However, I could understand the way David was using ‘abstract’. I think I’ve often used it in this colloquial sense as well. And in that sense it is often the opposite of empirical, which is seen as colloquially ‘concrete’. Given my arrogance, I — of course — assume that my current conception of ‘abstract’ is the correct one, and the colloquial sense is wrong. To test myself: in this post, I will attempt to define both what ‘abstract’ means and how it is used colloquially. As a case study, I will use the game assay that David and I disagreed about.

This is a particularly useful exercise for me because it lets me make better sense of how two very different-seeming aspects of my work — the theoretical versus the empirical — are both abstractions. It also lets me think about when simple models are abstract and when they’re ‘just’ toys.

## 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.

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. ## 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). ## 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. ## 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.

## Evolutionary dynamics of acid and VEGF production in tumours

Today was my presentation day at ECMTB/SMB 2016. I spoke in David Basanta’s mini-symposium on the games that cancer cells play and postered during the poster session. The mini-symposium started with a brief intro from David, and had 25 minute talks from Jacob Scott, myself, Alexander Anderson, and John Nagy. David, Jake, Sandy, and John are some of the top mathematical oncologists and really drew a crowd, so I felt privileged at the opportunity to address that crowd. It was also just fun to see lots of familiar faces in the same place.

A crowded room by the end of Sandy’s presentation.

My talk was focused on two projects. The first part was the advertised “Evolutionary dynamics of acid and VEGF production in tumours” that I’ve been working on with Robert Vander Velde, Jake, and David. The second part — and my poster later in the day — was the additional “(+ measuring games in non-small cell lung cancer)” based on work with Jeffrey Peacock, Andriy Marusyk, and Jake. You can download my slides here (also the poster), but they are probably hard to make sense of without a presentation. I had intended to have a preprint out on this prior to today, but it will follow next week instead. Since there are already many blog posts about the double goods project on TheEGG, in this post I will organize them into a single annotated linkdex.

## Modeling influenza at ECMTB/SMB 2016

This week, I am at the University of Nottingham for the joint meeting of the Society of Mathematical Biology and the European Conference on Mathematical and Theoretical Biology — ECMTB/SMB 2016. It is a huge meeting, with over 800 delegates in attendance, 308 half-hour mini-symposium talks, 264 twenty-minute contributed talks, 190 posters, 7 prize talks, 7 plenary talks, and 1 public lecture. With seventeen to eighteen sessions running in parallel, it is impossible to see more than a tiny fraction of the content. And impossible for me to give you a comprehensive account of the event. However, I did want to share some moments from this week. If you are at ECMTB and want to share some of your highlights for TheEGG then let me know, and we can have you guest post.

I did not come to Nottingham alone. Above is a photo of current/recent Moffitteers that made their way to the meeting this year.

On the train ride to Nottingham, I needed to hear some success stories of mathematical biology. One of the ones that Dan Nichol volunteered was the SIR-model for controlling the spread of infectious disease. This is a simple system of ODEs with three compartments corresponding to the infection status of individuals in the population: susceptible (S), infectious (I), recovered (R). It is given by the following equations

\begin{aligned} \dot{S} & = - \beta I S \\ \dot{I} & = \beta I S - \gamma I \\ \dot{R} & = \gamma I, \end{aligned}

where $\beta$ and $\gamma$ are usually taken to be constants dependent on the pathogen, and the total number of individuals $N = S + I + R$ is an invariant of the dynamics.

As the replicator dynamics are to evolutionary game theory, the SIR-model is to epidemiology. And it was where Julia Gog opened the conference with her plenary on the challenges of modeling infectious disease. In this post, I will briefly touch on her extensions of the SIR-model and how she used it to look at the 2009 swine flu outbreak in the US.