Friday, November 14, 2014

Mathematical Oncology: an introduction given at a Moffitt Cancer Center Radiation Oncology CME conference

Today at Moffitt Cancer Center I'm giving a short talk about Mathematical Oncology for a continuing medical education aimed at medical physicists and dosimetrists - though I think the talk is available to most folks with an interest in science and maths. It's a short talk (30 minutes) in which I hope to introduce the field, show some of the tools we use, and give a short example or two. I feel that this audience, in particular, is important to address because they have the skills needed to think like modellers, and work in cancer EVERY DAY.

My hope is to spread awareness of mathematical oncology, but also to lure some clever folks across the street from the clinic to the laboratory!

There are a host of great talks going on, many of which have their slides on line (I've been told) on topics as broad as #proton therapy, #StereotacticBodyRadiation, #cyberknife, #radiation toxicity, #HIV and cancer and more.

A full agenda can be seen here:

And here's my talk.

Tuesday, October 7, 2014

I see flowers & I think of metastasis: or how theoretical oncology has reshaped all of my thinking

I try to reserve weekends (or at least the hours of 8am to 8pm on the weekends) for time with my kids. I've got a little boy named Rhys, who is just now starting to learn language (he's about 18 months ago, really fun age) and a precocious little girl named Maren who is five and a half. I grew up either in a house full of books or out in the woods - my mom is a librarian and gardener and my dad is an English teacher, novelist and outdoorsman. Given this background, it is no wonder I still pay double most of my friend when I move because of the sheer weight of books my wife and I carry around, and also that I continue to love being outside.

My kids however, have a mom who was an occupational therapist and is now a photographer (gorgeous pics of our kids and other stuff on her page) and a dad who is a theoretical oncologist. So it shouldn't be surprising that my daughter doesn't mind a little gore, indeed she likes watching necropsies (thanks #thebrainscoop)

a Tweet which actually ended up in an article about Dana Scully from the #xfiles, Emilie Graslie from #thebrainscoop and the girl from the #BigBangTheory which you can read here:

and that we spend more time looking at Netter's anatomy book than almost anything else.  A few weeks ago, we busted out my microscope from medical school and I ordered a cool set of slides of amphibian and fish anatomy. She spent a few hours just fascinated and has subsequently asked to look at a ton of stuff under the scope (blue jay feathers are really fun - try it with the light from below, and then turn off the light and shine a light from above... great lesson on refraction).

That's her doing her best Ramon y Cajal impression on the left, and a tadpole stained (with H&E?) on the right. So, anyways, last weekend, we were trying to figure out what to do while her brother took a nap, and decided to see what we could see in the tanks of some of the bromeliads at the end of our street. We had watched a great David Attenborough documentary (oh yeah, they're pen pals)
in which we learned that lots of micro-animals can live in bromeliad tanks.

Neither of us could have been happier, however, than when we saw this little beauty under the scope (or, I should say \mathcal{O}(100) of them)

I turned immediate to twitter to ask my friends what it was, and was immediately told it was an #ostracod, most likely Elpidia bromeliarium. I dug a little more into it and there is actually only one species of these described in Florida, and many new species are found all the time (most recently in the Honduran cloud forest - just last year!). So, needless to say we are pretty excited about the possibility of having found a new species.

What really got me going though, was the question of how these things get around?! There is only the one stand of bromeliads in my whole neighbourhood, and these little crustaceans can't move purposefully outside of even the tank they start in! Here is an early description of them I found from a journal in the 50s:

Then, on the same day, someone tweeted about a new computational study of 'jump dispersal' vs. 'rafting' a mechanisms for animals/plants to move over large distances (from island to island, say) and I started thinking about the problem of metastatic disease. When animals or plants 'raft' from one place to another (this is often called Oceanic dispersal as well), they are often swept from river banks with a hunk of vegetation or soil, and often more than one animal (especially for sexually reproducing creatures this is very important). I remember a PNAS paper in which the researchers (using a totally medieval experimental technique where they sewed two mice together - seriously) found that many successful metastases brought their own soil with them (in this case non-cancerous cells to support the metastatic seeds).

Taken from:
There is more and more literature these days suggesting that it is clumps of circulating tumour cells that cause metastasis, not single cells (also a nice paper from my friend and collaborator, Peter Kuhn - lab page here). These clumps seem analogous to me to the rafts that other species might use, and could even be formed in the same way - in tumour associated mosaic vessels - there could certainly be a 'sweeping off' of a large clump of cells. If one disturbs the smoothness of a healthy vessel wall, there will be a disturbance in the otherwise (pretty close to) laminar flow and eddys will form and severely change the stress profile in the flowing fluid, creating a situation in which a chunk of cells could easily break free.

If true, this *sort of* obviates some of the modelling efforts that +Philip Gerlee and I (and others) have done considering the fate of single cells, but that work could certainly be reparameterised to consider the shedding rate of these clumps. My hypothesis would be that the results are quite similar, as the shedding rate would go down, but the chance of colonisation (given a clump landing somewhere) would be much higher.

Some other issues, like the Allee effect, could be overcome by this. Further, it offers some different ideas about therapeutics/preventatives. I wonder, for example, if there is any data on (non-liver) metastases in patients with Greenfield filters with colorectal cancer?

As for the little Elpidia - I found a cool study that shows, as +Benjamin Werner suggested, that they can survive in the guts of a number of creatures, so that's probably how they get around...

Anyways... ostracods, cancer, discuss.

n.b. there has been some interesting discussion on this thread already from a shorter post here:

Monday, October 6, 2014

Memantine and WBRT

After the whole brain radiation review that my collaborators and I just published came out, my friend and colleague, Jack West, put a nice post up on his website Cancer Grace about it and asked a follow up question on twitter:

He was referring to the recent Radiation Therapy Oncology Group's trial of memantine (a drug for dementia) given during whole brain radiation: RTOG0614.  So, to answer, I polled a couple of my friends who do nothing but neuro-oncology and reread the results of the trial (not out in published form yet, just as an abstract (paper #1 on this page) and the full talk from ASTRO).

As a quick summary: Whole brain radiation therapy (WBRT) is a treatment given to patients who have metastatic cancer in their brains.  There are a number of situations in which WBRT is given and it improves survival and significantly improves the life of patients.  On the downside, it has been shown to cause cognitive decline with as many as 60% of patients exhibiting measurable decline at 4 months after WBRT.  So, to combat this, a trial of memantine during and immediately after WBRT, an NMDA-receptor blocker used to treat Alzheimer's dementia was proposed and carried out.

In this trial, about 500 patients were enrolled, stratified by their RTOG brain metastasis RPA class (they only enrolled class 1 and 2 patients) and given either 20mg of memantine or placebo daily for 24 weeks.  A lot of their patients weren't able to be properly analyzed because of issues with survival (sadly, to be expected in this population), but those who were evaluable (~150) took a battery of 6 different cognitive tests.  The primary endpoint was performance on a specific test at the 24 week point, the e Hopkins Verbal Learning Test-Revised Delayed Recall (HVLT-R DR) and there was NOT a significant difference in the results of this (but it 'teetered on the edge of significance', with a p-value of 0.059).  Now, don't get me started on p-values.  Oops, too late.

The all holy p<0.05 is an arbitrary cutoff level by which we determine 'significance'.  I say again, arbitrary.  What it has become, I fear, is a gold-standard for a 'positive study'.  So in the case of this one, which technically did not meet its primary end point, many people are not swayed, because p wasn't less than or equal to 0.05.  the secondary endpoint, cognitive decline (a measure using several other of the tests) was met with p=0.01 and, crucially, there were no difference in side effects or survival. My *suspicion* is that the primary endpoint will be met if they can accrue (and analyze) another 50 patients, and this debate will end. However, until then, the jury is out.

Personally though, even though it failed to meet its primary end point, I will be recommending memantine to patients in a favorable RPA class getting WBRT, or at the very least having this discussion with my patient.

As an aside, the two Neuro specialists I polled had opposite answers, so it is fair to say that this remains in the undetermined category. But, the drug has been shown to be safe, and now *likely* efficacious. In a situation where we don't have other options, I'm sold.

Saturday, August 30, 2014

A new lymph node station in lung cancer?

Earlier this week in our morning didactics session we had an interesting discussion about advanced stage non-small cell lung cancer (NSCLC). Now, there is certainly a LOT to discuss about advanced stage NSCLC, and there is a lot of uncertainty in how to treat it with the multitude of new targetted agents coming on the market for mutations like ALK, KRAS, N-RAS, BRAF, EGFR, etc...  and the trials that have been run are often difficult to interpret because of changes in standard of care, stage migration due to novel imaging modalities (PET) and other things.

To add to all the uncertainty in treatment, the staging guidelines (AJCC in this case) can change. When I started my residency in 2009, we were on the 6th edition, and now it's the 7th. While the changes are usually small, they matter, because the trials that are now having results reported were often stratified using earlier editions of the staging guidelines, once again clouding the picture for patients needing treatment decisions today.

One thing that hasn't changed, and never will (?) however, is the location of nodal stations. Right? Maybe not! As a refresher, we care about a number of nodal stations when staging lung cancer. Here is the picture we all know and love (also available from the AJCC in poster form here):

Please direct your attention to the lymph node station labelled #7 - this is the sub-carinal station, and one that is often involved, and often biopsied because of the relative ease of access (bronchoscopically). Notice it is, by definition N2. However, it is also considered mediastinal. 

Now, this is all well and good, until you have a patient present, as we did at our cancer center several weeks ago with a Left sided T2 NSCLC with station 7 involved TO THE RIGHT OF MIDLINE. We went through the imaging carefully, it was NOT station 8R, it was station 7, creeping down and crossing midline to the RIGHT.

So, now the patient has, by one definition, T2N2 disease (there were no other contralateral nodes or other nodes to make him N3) by virtue of his involvement of station 7. HOWEVER, he could also have T2N3 disease by virtue of having contralateral mediastinal involvement! This is not a trivial difference as it is the difference between IIIA and IIIB, resectable and unresectable.

What to do? Well, he had poor performance status, so surgery was out either way, so we opted or combined, definitive chemo-radiation. However, this uncertainly raise the possibility of a need for more detail in the staging system. Sort of in jest, we proposed a change for the 8th edition - maybe we should have a station 7.5R/L dichotomy for significant involvement, or possibly a 7C/R/L trichotomy?

Saturday, August 2, 2014

Re-entry into the clinic and my first evolution paper!

Sorry for the long radio silence - I re-entered my residency after a 3 year hiatus to pursue full time research and things have been busier than anticipated. While I am on a light rotation (sarcoma), which requires only 50% of my time actually in clinic, I had forgotten what being a #resident is like, and more importantly, what having a pager is like!!!

My personal research efforts have slowed somewhat - with my efforts now divided between the clinic, being a dad and thesis writing. I've changed my focus to writing up what I have currently, rather than chasing after new results, so I haven't much to report. A student I'm working with, however, +Daniel Nichol , recently finished up a paper that he and I have been working on for some time. He is going to write a full blog post about the work, but this will take some time. In the mean time, I thought I'd at least let the community know we've finally submitted our paper to the +bioRxiv Preprints site, as well as a journal (contemporaneously), which you can find here:

In this paper, my first personal foray in theoretical #evolution we build on theory from some exciting theoretical and experimental papers from Steven Weinreich (Weinreich et al. Science) and +Jeff Gore (Tan et al. PRL) to explore the concept of 'steering' evolution as a method of preventing the emergence of resistant strains of bacteria (or cancer!).

I look forward to putting Dan's proper post up, but until then, enjoy the #preprint - we welcome comments!

We were flattered, as well, to see another blog pick up our preprint - yet another reason to use the bioRxiv or arXiv!

Thursday, June 26, 2014

Impact of vascular patterning on radiation response - contributed talk from ECMTB 2014

So - I meant to try to use +Camtasia Studio to record my voice during this talk, which would have made following along much easier, but somehow, the meeting was so chock-a-block with content and excellent social outings, that I failed to download and sort it out.  Next time...

For now, here is a short presentation that I gave as a contributed talk at #ECMTB2014 in Goteborg.  It represents the meat of the second chapter of my growing (fingers crossed) DPhil thesis. My hope is that by finding a metric (Ripley's K) that predicts radiation response in our CA model (based on a simplification of a CA I worked on previously with +David Basanta which we published here), that we (or someone!) could translate this into histopathologic sections from patient samples.

This is essentially an extension to a poster I presented at the #PSOC meeting in DC in early April which I blogged about previously.  Please feel free to ask questions or make comments. I'll let everyone know once there is a proper #preprint available, and in the mean time I'll try to learn to use camtasia.

'Till then, here's the presentation:

Monday, June 23, 2014

ECMTB 2014 in Goteborg, Sweden

I've just returned from nearly two weeks in the UK and Sweden, visiting friends and colleagues in both countries. The impetus for the trip was the once-every-three-years meeting of the European Society of Mathematical and Theoretical Biology called the European Conference of Mathematical and Theoretical Biology (ECMTB).  I first attended this meeting in Krakow, Poland (thanks to the futuristic vision of +Alexander Anderson ), before I even began my DPhil, and found a true intellectual home. This is an unbelievable group of people - intelligent, kind, fun loving and open minded.

The scientific content for this meeting was excellent (and can be found here) and included many parallel sessions of contributed talks, a poster session as well as member organized minisymposia (I hosted two, which I will blog about separately). There was a lot of activity in the +Twitter sphere recording both the scientific content as well as much of the social activity of the meeting - which are both, I firmly believe, are equally important to the success of a meeting.

I have storified the tweetcast of the meeting and social events, and will embed it below, but I also wanted to take a moment to thank +Torbj√∂rn Lundh and +Philip Gerlee and the rest of the organizers for a throughful and beautifully organized meeting. Everyone to whom I spoke had only nice things to say - the only complaint being that there wasn't enough time to see all the amazing content! Thank you so much for your hard work.

Take a moment to scan what's below - there is lots of linked content and interesting people. Also, keep your eyes out for a group (pro-con) post on tweetcasting on the WCMBlog in the coming days.

Sunday, May 25, 2014

A success story for Warburg's Lens

I've been travelling a lot of late, which I'll blog about on its own in a bit (including a 'best of the best' coffee machines post), but I heard a story from a friend, which triggered a memory which I want to share. It took a moment, but I realised that a whole chain of events that I was unaware of, yet intimately involved in) added up to a success story for Warburg's Lens, the theoretical oncology preprint discussion forum that some colleagues and I started to try to speed up the process of scientific discussion.

So the story goes like this:

I was trolling the qBio section of the arXiv, as you do on a Friday night, looking for interesting papers. For the record, I also always scan the +bioRxiv Preprints. On this night, I came across one from one of my favorite authors, +Arne Traulsen, who has an evolutionary theory group at the Max Planck Institute in Plon, Germany. The #preprint, entitled, Cancer initiation with epistatic interactions between driver and passenger mutations, seemed like a very interesting one, so I put it on Warburg's Lens for discussion. It generated some nice discussion on the site which even included the authors, who were able to defend some of the points, but also take on board some very relevant (non-anonymous) feedback.

Fast forward a bit, and I'm minding my own business trying to get a job, and I get a request from a journal to review an article.... lo and behold it is the same one we are talking about. For various reasons, I declined to review it, but I remembered that there were some very constructive criticisms from people on Warburg's Lens (people who have published significant works in this direct area), so I knew who I could suggest as a replacement reviewer, which I did. Readers won't have a problem guessing who any of the anonymous people are, but I will not divulge that here.

Fast forward again, and I'm visiting some colleagues in Boston (again, post to follow, there was wide #heterogeneity in coffee machines) and a friend mentioned that this great paper that he had reviewed just came out...  and on the same day, my colleague and supervisor, +Alex Fletcher sent me an email notifying me of the paper, which is now out, and you can find it online here, but of course, I can't get it at home without dropping $40. I am eager to read the paper and compare it to the #preprint.

Either way, congrats to +Arne Traulsen et al. on the nice paper and thanks to all who contribute to the discussion on Warburg's Lens - and it's inspiration website, Haldane's Sieve. Keep submitting your #preprints to repositories like the arXiv and +bioRxiv Preprints, keep doing good #openscience. This seems like a win for everyone.

Also, lest I forget, cheers to the Journal of Theoretical Biology for being cool with preprints. Let's keep adding to the list.  This is a tangible example of how preprint servers help EVERYONE, even the journals. We got faster, more on target review, because of the preprint. A list of journals and their preprint policies can be found here:

Wednesday, April 30, 2014

My visit to the Mathematical Neuro-Oncology group at NorthWestern and the talk I gave about glioblastoma evolutionary dynamics and metastasis

I recently was honored by an invitation to visit Chicago and present some of my recent research to my friends and collaborators in a new group formed there by +Kristin Swanson called Mathematical Neuro-Oncology. I spent my time visiting their new, beautiful lab;

celebrating +Russ Rockne's transition;

having some coffee;

visiting my roots;

finding out that a paper long in the works, based on an opinion piece I wrote a few years ago about the effects of the #IDH1 mutation in secondary #glioblastoma, is finally in press at Neuro-Oncology (aside: Somehow there is an editorial written about it that is available (if you PAY, which I haven't yet), but the article is not yet itself available); listening to +Kristin Swanson practice for her +TEDx talk, which I've heard went well, but haven't seen yet (more info here:; and actually giving a talk.

I couldn't decide what to talk about, and since the audience was going to be half computational neuro-oncologists (casual dress) and half general scientific/medical folks (white coast, ties, scrubs), I decided to give a talk in two parts - about a half an hour each.

I spent the first half hour talking about an exciting (to me at least) extension to previous work I've done here at IMO with +Alexander Anderson and +David Basanta and others on glioblastoma stem cells. I've blogged on this topic before, from posts about our recent paper in PLoS Comp Biology to a recent grant we submitted - which, frustratingly didn't get scored due to a very prototypical reviewer #3 (reviewers 1 and 2 gave us 1's 2's and 3's and reviewer #3 gave us 7's, 8's and 9's).

The second half I talked about the work I've done with +Philip Gerlee and +Alexander Anderson and others to understand how a filter-flow paradigm of metastatic spread can help us understand (and intervene) in the process of #metastasis itself. We've published most of this work as a perspective piece in Nature Reviews Cancer, a test of the self-seeding hypothesis in J. Roy. Soc. Interface, a review in a Springer textbook (pre-print here) and recently, a more clinically oriented piece under review at Clinical and Experimental Metastasis (you can see a pre-print here on the +bioRxiv Preprints site). Both I and Philip Gerlee have blogged about it (including a shared post here in response to a Cancer Research UK blog post which we took exception to (at least to parts of it)) in the past as well.

So - anyways, here are the slides. The first half is work in progress, and we're pretty excited about it. I'd love to know if anyone has any feedback.

Sunday, April 6, 2014

5th Annual (final?) Physical Sciences in Oncology Centers meeting at the NCI

I just got back from 3 days at the National Cancer Institute for the (final?) meeting of the Physical Science in Oncology Centers. It hopefully isn't the REAL final meeting, but it is the final one as we know the PSOCs, as they are changing drastically in the way that they fund folks - in ways that haven't been entirely decided yet.  Either way, I've been attending these meetings since the beginning, and they have been quite important as formative experiences for me: showing me that outside the box thinking is OK (even encouraged) in cancer research, and that being a non-standard cancer biologists can be a way forward.

Anyways, it was a great meeting, with interesting talks ranging from origin of life, to mouse modeling to evolutionary game theory. There was a young investigator session (which I missed, but heard was really good) and a poster session, where I gave this poster -
As always, there were lots of great opportunities for networking, catching up with old friends, and making new ones. I storified the tweetcasting under the hashtag #PhysOnc (it was lively) to give you a flavor of the meeting. So, here that is:

Saturday, March 8, 2014

The role of mathematics in oncology - a discussion

A few weeks ago, my friend and colleague +Philip Gerlee wrote a post on his blog with about the role of mathematics in oncology in which he generally suggested that our role, to date, as mathematical/theoretical oncologists has been to help see old data in new ways.  In the post he said further that there has yet to be a 'seminal paper' in the field that has changed the way that biologists (or clinicians) think about a problem or disease. In an addition to the post, at the suggestion of another friend and colleague, +Heiko Enderling, Philip added an errata, which suggested that maybe he was wrong, and that maybe an early paper on chronic myelogenous leukemia (which you can find our more about here) represented the 'seminal paper' that we needed.

I commented that, while I thought that paper added valuable insight to the field, that it hadn't really changed the way we think of (or treat) the disease. This comment kick-started a much more cogent, and thorough, blog post from +Artem Kaznatcheev

which was re-blogged and further discussed by +David Basanta on his blog, cancerevo.

I think that this debate is an important one.  As our field, mathematical oncology, is still young, defining our role is extremely important, especially for the new generation, as only by understanding our role can we measure our success and plan for the future. While I'm working as hard as I can to finish my DPhil at the Wolfson Centre for Mathematical Biology, I'm excited to think about trying to build a group centered around meeting these goals. Other fields of mathematical biology have better established roles (take for example, developmental biology in which many important advances have been made by theorists, like our own +Ruth Baker and her mathematical model of the clock and wavefront model, for instance), and I fear we'll lose promising theorists to this field (I'm talking to you +Alex Fletcher) if we don't better define our role.

So, take a look at the discussions and posts I've linked above, have a read and think, and chime in.

Tuesday, January 14, 2014

An Evolutionary Game to study the cancer stem cell hierarchy

So, I'm going to take a page out of my friend and colleague +Artem Kaznatcheev 's playbook and write a blog post about a project that I'm nearing the start of.  My DPhil thesis is centered around the study of the 'cancer stem cell' hypothesis, and how it affects tumour progression. You might remember a post earlier about an agent based model we've built to study this, and they'll be more in the future, covering other aspects such as radiobiologic response and niche evolution.  The first paper should be out soon in PLoS Computational Biology, and in the mean time there is a #preprint on the #bioRxiv here.

I've been slamming my head against the wall for the past several weeks working to write up the model in the form of a thesis chapter, which I'm finding is VERY different than writing a paper (at least for Oxford's Centre for Mathematical Biology).  So, as I can't stand it any more, I'm going to write this post about what I'm planning to be the final research chapter in my thesis - an exploration of plasticity in the cancer stem-cell phenotype using Evolutionary Game Theory (EGT).  EGT is a technique that has been used for half a century or so to study the evolutionary dynamics of populations containing species (or players) with different life-strategies (called payoffs).  It differs from standard Game Theory in that players can't change strategies, but instead, their frequency in the population will change based on the relative fitness as governed by the replicator equation.

We have used this technique in the past to study a few scenarios in cancer - specifically: +David Basanta and +Alexander Anderson and some collaborators from Vanderbilt studied the effect of therapy on prostate cancers made up of populations of cells independent and dependent on the stroma, which you can read here; and then we studied the role of IDH1 mutated glioma cells in glioblastoma with +Russ Rockne and +Kristin Swanson.  More recently, +David Basanta and +Artem Kaznatcheev and I studied what happens at the edge of a tumour using a method developed by Ohtsuki and Nowak which Artem has blogged about a fair bit to try to get around the limiting assumption that is typical of evolutionary games of the population being well-mixed (recently updated preprint).

Phew - that was a long introduction. Anyways, I'm eager to do some EGT in my thesis, and no one has tried to make sense of cancer stem-cell plasticity with this technique, so I figure I'll give it a go. We're interested in what sort of conditions would result in promotion of the stem phenotype, why the stem fraction would be heterogeneous and how different sorts of stem-cell niches would affect this fraction. These are good kinds of questions to ask using EGT as the end result is (typically) ranges in parameter space that map to certain population proportions in the long run (called the Evolutionary Stable State which you can read about here).

So - what's the game then?  Well, we've thought long and hard about how to structure this sort of game. We've gone back and forth thinking about pitting one stem cell against another, different types of tumours (with different stem parameters) against one another, but have recently settled on trying to pit the stem cells vs. plastic daughters vs. non-plastic daughters.  We're going to consider some intriguing data from our collaborator +Anita Hjelmeland about the role of IL-6 in promoting the stem phenotype and try to make some sense of all of this!  We begin by thinking about the allowable phenotypic transitions and population changes as stem cells either self-renew (probability s) or divide asymmetrically to form a non-stem daughter and maintain their population number.  The plastic progenitors can also self-renew (probability a) or differentiate (d) or dedifferentiate back into stem cells (1-a-d). You can see a schematic of this in the figure below:

We decided to move away from the standard formulations of EGT in this respect, and we consider these sorts of divisions (ones that increase or decrease a population) as being fitness payoffs. And, as I said we'd try to consider the effects of IL-6 which +Anita Hjelmeland and crew wrote about, we've added in an asymmetric cost (c) and benefit (b). In their paper, they found that both stem and non-stem cells produced IL-6, but that only stem cells benefitted from its presence.  So, our final payoff table looks something like this:

hmm... you can't really read that - but I can't NOT include a picture of the chalk board, so there it is. Here's the payoff table we think we're going to go with.  Now listen, if you are an EGT nerd (I'm talking AT LEAST to you +Artem Kaznatcheev - PLEASE DO NOT ANALYZE THIS GAME, or if you do, keep it to yourself, I need a DPhil!).

Yes, I know there's a -c in every block and that I can simplify the game a bunch more.  No one is sure if the cost of producing IL-6 (c) is the same across cell types, so we're still thinking on it.

So - that's where I'm going to start.  With any luck we can learn something.  Worst case, I'll be able to make some pretty pictures and do some proper analysis.  Next post will be an analysis of the three 2x2 subgames, a la Artem's method (analyze, blog, analyze, blog, PAPER!).

More soon.  If you have feedback on the payoff table, I'd LOVE to hear it (BEFORE I start analyzing it).

ciao for now