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

Handling collaborative projects in the age of the cloud - how to manage without spending any money!

As a clinician cum scientist, I am almost always involved in collaborations with multi-disciplinary groups.  And, as an american who has done some training in the UK, many of those groups are NOWHERE REMOTELY NEAR one another.  To keep myself, and my collaborators sane, I've been constantly experimenting with different combinations of cloud based repositories so that we can all work on things together.

So, I started out with +Dropbox by itself, but quickly found that, without spending money, I quickly filled up my allotted space.  Even after totally maxing out the freebie upgrades (I think I have like 35Gb or something thanks to some promo at Oxford, referring everyone I know and being a shameless social media promoter - every Mb counts!), I still am limited.  So I added +SugarSync for my personal files, to clear off dropbox and leave it for just collaboration.  Well, that filled up pretty quick too, and as I haven't found sugarsync to be as easy to navigate as dropbox, I haven't worked as hard to maximize my space there.  I muddled along with these two but still struggled with things like version control and the desire for contemporaneous editing.  Which led to...

Google drive and google docs.  So, with google drive, you get 25Gb or something, but I started to get confused as to where things were.  When I wanted to collaborate real time though, I was stuck, as google docs was really the best thing going (and still is, for many things).  However, in the last few months, I discovered +writeLaTeX, which has really changed the way I do business.  This is a (mostly) free service (I haven't hit the wall yet, and it is pretty big considering that you don't store data there really) in which you can create, manage and edit LaTeX documents with as many people as you like. For me, as a mathematical biologist, this was great - so long as my collaborators were also theorists who were tex-savvy.  I first used it doing a little hack-a-thon with some friends that I blogged about before. Recently though, as in, in the last few days, they have added a Rich Text formatting layer which, I think, will change everything again.  No longer will I have to give the link to a document to my biological/clinical collaborator with the caveat 'just ignore everything that isn't text - squint a bit if you have to'.  Now, they can just go ahead and edit away just like they are in word or whatever, but I can come in behind and have the full functionality of LaTeX.  So that aspect seems solved.

**note - I LOVE writelatex, and you should check it out... and if you do, use this code and I get 50MB more space.  https://www.writelatex.com/signup?ref=5ed6049a8e70 **

The only issue left for me is, now that I'm cranking TONS of simulations in (what I hope is) the final push toward this whole PhD thing, how to work on a DATA-HOG of a project on two computers (I can't stay at work late because I want to go home to my super sweet little kids, but then I DO want to work after they go to bed without driving back to work) or to share this with someone else.  I thought, at first, that I'd just clear out my dropbox a bit, and try to be parsimonious with what I saved...  but, as the output for my simulations is \mathcal{O} 30Gb/simulation, this quickly became unfeasible.  Enter bittorrentsync - my saviour.  This little gem (free) lets you have a synced drive on as many computers as you like.  The freeing move here is that there is no cloud interaction, so there is NO SPACE LIMITATION.  (There is also no auto-backup for the same reason... but this is obviated if you use Time Machine or something similar).  All you do is download the software (a couple Mb's) and then, to set up a shared directory, it generates a 'secret' which you share with whomever you want to share.  The secret is a massive string of letters/numbers that is autogenerated - and I bet even the guy at xkcd.com would approve.

So, now I'm set and I don't have to think too hard.  I also don't forsee ever having to spend any money (until maybe I have a lab or my own and lots of people, but by then - if that time ever comes - I will have grant money to spend on such things...  ?).

Summary: I use dropbox for shared/travelling talks, figures, syncing my papers library, shared simple code (matlab, etc).  I use sugarsync for my personal documents (though I might phase this out...). I use writelatex for (now and going forward) ALL papers I write and bittorrent sync for shared working directories (also home/office syncing of working directories).

As an aside, dropbox has a cool feature - since everyone can modify things at will, they have a nice cloud backup system, which includes who the last person to interact with a document was, so in case your supervisor starts randomly deleting hunks of your thesis, you can call them on it - not naming any names...  +Alexander Anderson :)

To be fair, I don't think Sandy actually deleted this stuff... and I was able to recover it, but it was pretty funny :)

Guest post on the Oxford Centre for Maths Biology Blog

I wrote a post for my group's new blog on the importance of #preprints in science, and specifically on the new #bioRxiv.  Head on over and check it out:

http://wcmb-oxford.blogspot.com/2013/12/pre-print-servers-dangerous-ways-to.html

Investigating the effects of microenvironmental perturbation on a stem driven tumor

I've been interested in the cancer stem cell hypothesis for some time, a subject that my colleague +Heiko Enderling has been thinking about and modeling for some time (list of his pubs here). I first became interested in this concept before I became a DPhil student and member of the Integrated Mathematical Oncology group, when I was a clinical resident in radiation oncology at the Moffitt Cancer Center.  One of the first papers that I saw that truly scared me was a paper by Tamura and colleagues (abstract) that showed that recurrent glioblastomas had a significant increase in CD-133 staining (a stain commonly associated with stemness in this cancer and others), and that this increase is correlated with (maybe causes, jury yet out) an increase in aggressiveness of the recurrent tumor and a decrease in its sensitivity to treatment.

The standard rationale for the latter is that these special 'stem cells' have a higher intrinsic resistance to radiation therapy (which I don't argue), but I subsequently wrote down a series of simple (some might say Noddy) ODE models which suggested, at least to me, that there might also be a stem promoting effect of radiation.  Since then, I have found that this effect has been shown in breast cancer, and further, that there have been a number of microenvironmental perturbations that have been shown to do the same thing, though only in a qualitative way - many of these articles have had my collaborator, +Anita Hjelmeland as a co-author, and I talked about them quite a bit in a previous blog post on our recent R-01 submission.

When I first started on this problem from the theoretical standpoint, it was with ODE models, as I mentioned.  But since then, +David Basanta and +Alexander Anderson and I have worked to build a cellular automaton model of a stem-driven tumor which included blood vessels as sources of oxygen. We built this simple model to test if there were some sort of intrinsic/emergent change in the resultant tissue phenotype when the overall levels of oxygen supplied to it went down (when we reduced the density of the vessels).  Below you can see the schematic of our model system.  On the left is the canonical Cancer Stem Cell hypothesis (which I have major issues with...  more to come in a few weeks I hope) and on the right there is our CA model rules.

After much simulation and effort we found... in short, that no, there is not. Our initial, negative results, were frustrating, but after discussions with +Anita Hjelmeland and Prakash Chinnaiyan (a biologist and clinician, respectively) we found that the model was telling us more...  while we found little qualitative effect when we changed the vascular density, changing the instrinsic stem behavior parameters in the presence of a minimalistic environment revealed that there were only three major meta-phentypic behaviors possible: extinction, dormancy (homeostasis) and overgrowth as seen below.

Our frustration at not seeing the emergence of greater stem-fraction upon lowering the oxygen levels however, led to the rather obvious (in retrospect) conclusion that only through a modification of the symmetric division rate of the stem cells (modified by hypoxia) could this effect be recapitulated. Interestingly, this is a conclusion we had come to in the past using a simpler model system (ODEs) but it was never convincing (though there is a nice piece in J Theoretical Biology which gave me some confidence... here).  Initial testing of this hypothesis, by modification of the CA rules to include this change are striking - surrounding the area of hypoxia, we have an emergent stem cell niche.

Stem cells (red) emerge in areas surrounding necrosis (white/center) when the CA rules allow biased symmetric division in the presence of moderate hypoxia (right).

We have just begun exploring this phenomenon, and indeed there is quite a bit of work to do, both theoretically and experimentally, to validate and better characterize what is going on - so that's why we wrote an R-01.

Anyways, if you want more details, you can read the paper on the bioRxiv now, or in a few days on PLoS Computational Biology where it has been accepted and is nearing publication.  We've also made the baseline code freely available on sourceforge here.

If you have comments on the paper itself, please leave them on the bioRxiv site so anyone can see them (or wait to put them on the PLoS CB site). Ok, back to work.

A new pre-print server for biology: the bioRxiv

I've written a few posts in the past about the need for a pre-print server in biology, like the one that physics and maths have, in the arXiv, to speed up the rate of dissemination of information in science, and to help promote open access.  As a physicist by original training, posting my work before it is accepted or done has never seemed like a big deal - it is science after all, we're all wrong, all the time (but we're trying to get closer to the truth, AS A GROUP).

In my community, the theoretical (mathematical) oncology community, we have been able to get around the lack of a standard pre-print server as there is a quant-bio section to the current arXiv, but it is certainly not widely read, nor is it really what the folks at the arXiv want to support (but we thank them for doing so, mind you).  In fact, I once tried to get them to add a theoretical oncology section without success - prompting me to create Warburg's Lens - a discussion forum for pre-prints in math oncology.

With the advent of +PeerJ there has been at least one option, and another called CancerCommons has sprung up as well.  In the next several weeks, we'll have another option, the bioRxiv - run by the folks at Cold Spring Harbor - a highly respected biological institute in New York.  There have been a few attempts at this sort of thing before - Nature tried it once with its "preceedings", but it never took hold. I heard a rumor that this is because a lot of non-science was posted (thinly masked creationism and silly studies about herbal supplement pyramid schemes like Protandim).  So, the bioRxiv has a plan to prevent this:  they've asked a number of people to become "affiliates" whose job it is to screen the preprints to make sure that it is, at least, science.  There will be no judgement about merit, we're to leave that to the communities, but just to screen out non-science.  Anywho, I'll be splitting my pre-print posts between here and the physics arXiv from now on - depending on focus.  More clinical/biological papers will go to the bioRxiv, and more mathematical/methodological will go to the physics arXiv.  For Warburg's Lens, I'll troll both...

I hope you check out the bioRxiv, and, if you are doing work in the biological sciences, I hope you consider posting your work here as you submit to standard journals.  I did a poll recently on a friend's website, and found that the only thing really stopping biologists from posting was...  well...  NOTHING.  Mostly, it was habit and inertia.  So - let's change those.  Let's put our work out there early and often and let the scientific community do its thing!

Glioblastoma: Stem cells, plasticity and the niche(s). A summary and introduction to our R-01 submission.

I've had an interest, both clinically and scientifically, in glioblastoma for about 6 years.  This started out because I was given a project as a medical student looking at outcomes of treatment for elderly patients, but has continued and consumed more and more of my conscious and unconscious thought in the intervening years.  For a long time, patients over 70 weren't given the same care as their younger counterparts because it was felt that the treatment was too harsh for them.  This paradigm has begun to change, thanks in some part to the work I was a part of, but the outcomes remain very poor, for all patients.  While I had success in this initial clinical research (first two figs), I was frustrated at what I perceived as a lack of progress, and didn't feel that I was really contributing to this.  This feeling is really what pushed me into basic research...

Unsurprisingly, adding more therapy extends survival in the elderly.  Taken from:

Scott, J. G., Suh, J. H., Elson, P., Barnett, G. H., Vogelbaum, M. A., Peereboom, D. M., et al. (2011). Aggressive treatment is appropriate for glioblastoma multiforme patients 70 years old or older: a retrospective review of 206 cases. Neuro-oncology, 13(4), 428–436. doi:10.1093/neuonc/nor005

Anyways, my story aside, this post is supposed to be about this new research project. So, let me first provide some background. Glioblastoma is the most common primary malignancy of the brain in adults. It carries a poor prognosis of about 1.5-2 years from diagnosis - even with advanced surgery, radiation and chemotherapy.  The nature of this tumor is quite different from all others - it is incredibly invasive, with rogue cells appearing many centimeters from the primary mass.  This is different than most solid tumors, which typically have a sharp edge where the tumor stops and healthy tissue begins.  There may be some small number of cells that slip over, but usually surgeons are able to get a 'clean margin'.  This is not so in glioblastoma - even if the margin appears clean (no cells visible under the microscope), we know from prior experience that there are viable cells at quite a distance.  There is a famous surgical study from the 1930s where doctors removed THE ENTIRE HEMISPHERE of the brain in which these tumors resided, and the patients recurred on the other side (first reported by Dandy, JAMA 1928).

Recursive Partitioning Analysis showing prognostic subgroups for patients over 70.
Taken from: Scott, J. G., Bauchet, L., Fraum, T. J., Nayak, L., Cooper, A. R., Chao, S. T., et al. (2012). Recursive partitioning analysis of prognostic factors for glioblastoma patients aged 70 years or older. Cancer, 118(22), 5595–5600. doi:10.1002/cncr.27570

To combat this, we have tried treating patient's entire brains with radiation (whole brain radiation therapy), but were not able to control these distant recurrences using safe doses, and given every flavor of chemotherapy you can imagine.  Sadly, only one chemotherapy, temozolomide, has been shown to be effective, providing approximately a 6-8 week survival advantage - far from a home run.

Probably the most famous figure in all glioblastoma research - evidence that a chemotherapy significantly improved survival: by about 6 weeks.  Taken from: 

Stupp, R., Mason, W. P., Bent, M. J. V. D., Weller, M., Fisher, B., Taphoorn, M. J. B., et al. (2005). Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma. The New England journal of medicine, 352(10), 987–996. doi:10.1056/NEJMoa043330

So, our standard of care is to treat where the tumor was before surgery and a smallish margin around the edges, and hoping that our chemotherapy will take care of the more distant cells.  In 2004, a famous paper from Singh and colleagues identified a small subset of cells within a glioblastoma which seemed to be responsible for these recurrences - and these cells shared many attributes of non-cancer stem cells.  It turned out that these cells were more resistant to radiation - and this gave us hope: maybe we weren't curing these patients because we were targeting the wrong cells!  The field of glioma stem cell biology has advanced rapidly and many scientists are working on the problem.  A prominent group in this field is led by Jeremy Rich at the Cleveland Clinic's Lerner Research Institute.  They have made many advances, but recently their focus has been on the effect of physical/chemical factors within the 'microenvironment' of the tumor that promote these special 'stem' cells - for example acidity, low oxygen tension and low glucose levels.

One of the scientists from this lab in Cleveland, Anita Hjelmeland, recently took a faculty position at the University of Alabama in Birmingham, where they have a massive brain tumor center (called a SPORE) to continue her work.  She and I met when I was visiting her lab in Cleveland and gave a talk about some of the theory work that +David Basanta and I have done.  She and I hit it off, scientifically, and we decided to start a collaboration.  We've worked together now on a few different projects that are in various phases of development, and just yesterday, we submitted an R-01 (a large scale, 5 year grant) proposal that is led by Anita and David, with participation from myself, +Alexander Anderson and +Heiko Enderling.  We are hoping to leverage the strengths of her biological laboratory with our theoretical modeling techniques to try to make some progress against this cancer. Her work previously has shown, convincingly, that hyoxia (low oxygen levels), acidic pH and low glucose levels promote these 'stem' cells, but trying to understand how they all work together is a difficult task - especially in a living system.  This is where our computational models can help.

Anyways, we have our fingers crossed for the success of our grant, and I'll be sure to keep you updated as to our progress.  As a teaser, I am including a figure from our grant.  Mind you, this is unpublished preliminary data (SHARING IN SCIENCE IS GOOD!), so don't draw too many conclusions from it.

Taken from: 

Heddleston, J. M., Li, Z., Mclendon, R. E., Hjelmeland, A. B., & Rich, J. N. (2009). The hypoxic microenvironment maintains glioblastoma stem cells and promotes reprogramming towards a cancer stem cell phenotype. Cell cycle (Georgetown, Tex.), 8(20), 3274–3284.

Some background: it seems that these special 'stem' cells in the tumor preferentially live in special areas called 'niches'. These niches come in (at least) two different varieties, near to the vasculature, where nutrients are abundant, and near to areas of necrosis (cell death) where nutrients are scarce. This difference is intriguing and some observations have suggested that they might contribute to differences in treatment response.  So - the preliminary finding...  our model suggests that the physical microenvironmental history of these niches is very different, and that the evolutionary dynamics within them are as well!  If we can better understand how these niches are created and maintained, maybe we can make some inroads against the progression of this tumor.

Our model, center, has two different areas in which stem cells seem to reside - near to vessels, where the environment is stable, and near to the areas of necrosis, where the environment is harsh. (unpublished data)

So - wish us luck.  The model that we have extended to make the above prediction is under review at PLoS Computational Biology, but you can see a preprint here.  Anita has published a TON of papers on this subject, which you can find on pubmed.  David has also written several papers (a couple with me) on glioblastoma, but only the preprint so far on stem cells in this disease. Our resident stem cell modeling expert, +Heiko Enderling, will be of great help as well.  You can see his long publication record on his website.

Pint of Science, US

Wow - it's been a while since I wrote anything.  A combination of several academic visits from +Alex Fletcher and Anita Hjelmeland, trying desperately to make some headway on my thesis, and a teething toddler left this blogging effort at the bottom of the pile.  I've got a few posts I need to write to catch up, but I thought I'd start with this one.

Last year, a movement was started in the UK called pint of science who's stated mission is to bring top scientist into pubs to communicate their passion for science to everyman.  They began with 15 pubs in London, Oxford and Cambridge for a several days long festival to great acclaim.  The movement is now spreading, and my good friends +Parmvir Bahia, +David Basanta, +Arturo Araujo and new friend +Angela Rey decided to start the movement here in the US - aptly named, Pint of Science, US.  They have worked to find their own spin on the theme, and settled on holding both a live event, and also on a podcast, on a monthly basis.  The central theme is the same - communicate what it is that we do as scientists, and why we do it, to the folks with whom we live and work.

The first even was held two weeks ago today at the New World Brewery in Tampa, FL.  I was honored to be asked by my friends to be the first speaker.  This is both a good thing and a bad thing.  The expectations are low (or, undefined), but it is also a difficult ask, because there is no predetermined script to follow.  So, you'll notice some hems and hahs in my podcast.

PB doing the introduction...

The audience at this, the inaugural event, consisted entirely of friends and co-workers, so it felt a little strange telling my life story and trying to convince 'people' that mathematics can help to play a role in cancer research (as everyone knew my life story and DOES mathematical cancer research).  So, in some ways, this event was more difficult than any other event like this that I've done.  Strange to admit, but I was sweating bullets!

Anywho, after some gentle editing from the Pint of Science US team, a podcast emerged and the event was a success.  I had a great time participating, and look forward to the next even when I can have a pint and learn about some neuroscience from our friend Tom Taylor-Clark, at USF.

I certainly recommend coming to the event, and subscribing to the podcasts - which are available on iTunes as well as through the link here.  You can also follow Pint of Science US on G+ or on twitter @pintofscienceUS for updates.

Have a pint, talk about science.