Some fun with evolutionary graph theory - and application to cancer?

For a few years now I've been interested in evolutionary graph theory - a branch of mathematics at the nexus of evolutionary dynamics and graph theory. To my knowledge this was all kicked off by Martin Nowak and colleagues with the 2005 Nature paper:  Evolutionary Dynamics on Graphs. One of the coolest results was that certain graph topologies exhibit striking changes in probabilities of fixation (assuming a Moran process) - particularly symmetric graphs called 'stars'.

A beautiful follow on paper by our friends at the Max Planck for evolutionary biology, led by +Arne Traulsen showed that this amplification of probability of selection led to a dramatic increase in time to fixation - sort of balancing out the advantage. You can read more about this in this terse paper in the Royal Society B entitled: The effect of population structure on the rate of evolution.

Since reading these two papers, I have given a fair amount of thought to this problem, but have not come to any sensible conclusions. +Alex Fletcher and +David Basanta and I spent a week or so once coming up with some code to think about how a cancer cell might invade an epithelial sheet (a biological structure that is topologically lattice-like). We never really figured out where to go from there (still working on it!!!), but in the mean time, conversations with Laura Hindersin and Benedikt Bauer at Max Planck about Laura's Phd work (example paper here: Almost all random graphs are amplifiers of selection for birth-death processes, but suppressors of selection for death-birth processes) has sparked a lot of interesting thought and conversation.

Further, at the recent conference: Cancer Evolution Through Space and Time the conversation continued and we started talking more about 'mixed' topology structures. The conversation has continued on twitter, culminating with a new student in my lab +Sudhir Manickavel starting some work simulating evolution. Here's where our thinking is going:

Twitter crowdsource #graphtheory problem. [assuming a Moran process] pic.twitter.com/h5e6LLDasU

— Jacob G Scott (@CancerConnector) September 30, 2015

@CancerConnector @EvolTheoArne @dbasanta @ara_anderson The "ring" can't decide where it belongs... ;) pic.twitter.com/dZn9dSjDNv

— Benedikt Bauer (@EvolTheoBene) October 19, 2015

@EvolTheoBene why not proper mixed topology? (Plus/minus green edges-pardon white board #clinicday @LauraHindersin pic.twitter.com/1V1diJkzC7

— Jacob G Scott (@CancerConnector) October 19, 2015

@CancerConnector @EvolTheoArne @ara_anderson @dbasanta Nice idea, this is what the rank in fix prob looks like pic.twitter.com/pEW7rC4s5o

— Benedikt Bauer (@EvolTheoBene) October 22, 2015

Building his first adjacency matrix - new volunteer to Theory Division! #mathonco pic.twitter.com/CRlYuQSIet

— Jacob G Scott (@CancerConnector) October 16, 2015

When he first started considering this project +Sudhir Manickavel , a medical student asked of the Royal Society paper mentioned above:

"I read the paper and I found it interesting, especially the idea that even though star structured populations have a greater fixation probability it actually takes them longer to fix.

I do have one question about the paper, in reference to a tumor how would you define a tumor population as well mixed or star structured?" 

A great question...  to which I responded:

"What is the topology of an epithelial sheet? What is the topology of a colonic crypt?  Does the topology of the stem cell niche within the crypt differ from that of the walls of the crypt?  How would you characterize the topology of bone marrow? Or - in infectious diasese: Of a blood borne pathogen? Of a biofilm?"

And included a link to a Gatenby classic which opens with:

"The human body plays with evolutionary fire" and discusses the unique (changing) topology of the colonic crypt and how this may influece evolutionary dynamics...

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3744108/

Which seemed to sell him on the topic as just this morning, I looked in my dropbox, and it looks like +Sudhir Manickavel is making some progress (though there seems to be a missing node...  :) ):

initial condition plotted with networkx to study the moran process evolving on a 'mixed' topology structure... is it a ring or is it a star?

Anyways, the start of a fun project either way.

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:

Ecmtb2014 vascular patterning from University of Oxford, Moffitt Cancer Center

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 +Torbjörn 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.

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: http://www.tedxuchicago.com/kristin-swanson); 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.

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.

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

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.

A visitor, the resulting hackathon, and a nice result.

So, I was sitting in a pub in Oxford (the head of the River - gorgeous place and one that Lewis frequents), and I met this guy +Artem Kaznatcheev. No, he wasn't having a pint at the table next to me. No, he wasn't there for an academic visit.  I met him on twitter, because of a tweet from +Steven Strogatz about mathematics in biology.  Here's how it all began:

In there, we can also see the first thoughts about making this blog - about 6 months before I actually did it. Better late than never?

Anyways, +Artem Kaznatcheev and +David Basanta and I (and some others) started what is now a 10 month long conversation, mostly on Google+, in a community Artem started and we co-moderate, called Evolutionary Game Theory.  This conversation has covered topics (subsequently blogged about) ranging from understanding vs. predicting (followed up nicely by +Philip Gerlee in his blog here), games bacteria play (and a recent +Jeff Gore paper in PLoS Biology), connectors in science and, more recently, the topic of our original connection: the use of game theory in cancer.

The conversations have been lots of fun, we all think a bit differently, but have many of the same ideals about science, understanding and the uses of mathematics.  Further, we are all hopeless nerds and *cough* workaholics.  So, when Artem noticed that the conference he was going to (Swarmfest 2013) was near us, he jumped at the chance to come meet us and get some work done.  On his way down, he gave a couple of David's papers a detailed read through to get the lay of the land (and blogged about it - clever way to annotate things for yourself as well as manage a post).

So, here's the hackathon part.  Artem arrived Wednesday night and he and David worked into the wee hours.  He then came in to #IMO and they spent the day doing a full analytic treatment of a game David and I published in the British Journal of Cancer.  They then worked again into the wee hours at David's house.  I arrived from an out of town trip the next day (Friday).  Artem came in to IMO and gave a talk (which we managed to broadcast on G+, something we hope to continue, but with better sound quality, any ideas on a bluetooth mic?).

Here's me and Chandler looking interested.  Also, you can see we had 4 or 5 others from all over, Germany, Oxford and I don't know where else... 

After his talk, we spent the afternoon identifying a tight question: in a growing tomour, what would change in a simple game or proliferative vs. motile cells between the middle and the edge, if anything?

One of the difficulties in EGT is that neighborhoods and population structure is not considered, indeed, it is assumed that the population is inviscid (well mixed).  A great paper from Martin Nowak at Harvard gave us a way to think about effective neighborhood sizes (formally, how to understand changing game dynamics on graphs of differing, but regular, degree).  This has some obvious applications to growing tumours - when they hit a basement membrane or an organ capsule they go from growing in 'free 3-d space' (neighbors on all sides) to growing almost in 2-d, against a wall (with neighbors only on one 'side').

So, we spent the rest of friday afternoon doing some analysis

Then, on Friday night, we celebrated by buying a bunch of redbulls and working 'till 2am at my house.  I dropped him off at his hotel, then picked him up for a late breakfast and we worked, using this great new on-line app we found +writeLaTeX (which is AWESOME) and started a manuscript.  At dinner time, we broke company...  Then, Saturday night, we really blew off some steam - and made the figures for the paper.  Dropped off at his hotel around 2am, he was picked up by David the next morning and they worked until his plane left.

So, that was the hackathon.  The result, we are proud to announce, is a paper, done and dusted, beginning to end, in 15 days, with the lion's share of the work done in the first 4 days (about 48 hours of which saw the three of us working full on).  To be fair, we thought hard about the question in conversations for several months, and the groundwork had been laid by previous papers, but really, this felt like doing theory the way you're meant to.  It felt inspired.  And, I think, this is the best paper I've been a part of so far.  But, don't take my word for it, check out the preprint, just released on the arXiv today:

http://arxiv.org/abs/1307.6914

We also have submitted it, and it is now under consideration at the Proceedings of the Royal Society, Series B.  While we were motivated by a cancer scenario, we feel the result applies more broadly to biology than many of our previous papers, and so have targeted a broader biological journal.  And, PRS B does publish theory, and has recently published some interesting work from +Arne Traulsen's group at Max Planck on evolution in structured populations, so it seemed like we have a chance...  we'll see.

After this experience, we hope to weave hackathons like this into our schedule more often.  It certainly isn't something I (or my family) could tolerate every week, but it was fun and highly productive and we'll try to do it again soon.

Anyways, we'd love feedback on the paper.  Artem has a more technical post today about the work and some future directions which you can read here.

Visit to Summer Science Program in Socorro, NM

About a year and a half ago, after my talk at TEDMED 2012, I got a call from a medical oncologist asking if I would come to visit a summer camp in the desert of New Mexico that featured a bunch of really smart kids and astrophysics. This sounded right up my alley (I love nerds, and I love stars), but the trip from Oxford to New Mexico seemed a little bit...  far.  So, I said I was interested, but maybe we could talk next year, when I was back in Tampa in IMO - which I promptly forgot about.  Thankfully, they didn't forget, and a year later, I got the call again.  So I packed up and headed for the Summer Science Program's, Socorro, New Mexico campus (on the campus of New Mexico tech, home of the Miners and well known for excellent work on explosives!).

As I left the rental car place in the Albuquerque airport, I asked the attendant how to get to 25 South and he said:

"You mean 25 North, there isn't anything to the south"

Which is how I knew it was the right direction...

After arriving, I was met at my hotel by the site director, Barb, and I asked to go up to the telescope to see the kids doing their observations.  This camp is set up in a really cool way, they spend 6 hours a day in the classroom doing intensive math/physics and computer science (Python) coursework.  They are split into teams of three, and at the very beginning they choose a near earth asteroid (the way they choose the asteroids is kind of a funny story, but maybe one of the students will comment with how that works...).  The teams then get a certain amount of telescope time, during which they take measurements of their asteroid's position.  They are then expected to do the math and write up some code to predict the orbit - which they then share with some astrophysicists at Harvard.  Really cool - not just taking courses and playing with telescopes, but DOING MEANINGFUL SCIENCE. Needless to say, I didn't fly all the way to NM to just give a talk, so at around midnight, I wandered up to the observatory.  It was DARK (perfect) and Barb got out a flashlight, which I asked her to extinguish so I could enjoy the darkness...  she demurred suggesting that we needed it to see any snakes in the path.

Me:  Snakes, pshaw...  wait, you mean like that one?

She ran away, and I snapped this pic - can anyone ID it?  Not the best pic - iPhone flash sucks...  its head was narrow, like a non-venomous snake, but I don't know my high desert fauna...  little help?

We finally got to the telescope and found the group observing.

They weren't able to see their asteroid this night, but they showed me a beautiful globular cluster (pictured) and a spiral galaxy that they found.  How cool. 

The TA who was there gave me a short tour and I found out that he is starting his DPhil in Oxford next year, at Summerville college (right next to the CMB, my home!) doing condensed matter physics.  Small world.

I finally crashed and awoke to take a short run and saw this really cool 'M' in the hills.  This delighted my daughter (Maren - of course the 'M' was for Maren!) who thought of the Thomas the tank engine episode about the Man in the hills.  It turns out it is for the NM tech Miners, but I like the M in the hills better.

Anyways, after my run, I went up to the campus and set up to give my talk,.which you can see here:



 Beyond an introduction into the uses of mathematics in cancer research (and theoretical biology in general) I focused on the need for taking risks in science, and how we ought not shy away from creative thinking.  Further, I talked a bit about my tortuous career path and how having done a ton of different things, and not just following a straight arrow course, had informed my science and my life in general. After the talk, they gave me a sweet green SSP engraved laser pointer (THANKS!) and I had lunch with the students and a chat afterwards...  it was at this point that I started ranting about open access science (I was overtired) and tried to convince them to put the findings from their summer research onto the arXiv (might need an endorsement for astrophysics...anyone willing to help?) and their asteroid tracking code onto github.  Why not!?

Here's the pic.  I was overjoyed to see a large cadre of girls at the camp - a good sign for our future!  I am certainly going to keep this place, a well-kept secret, in mind for when my kiddos are in high school.  I just wish I had had an opportunity like this - and I'm amazed that I had never heard of it.  My high school teacher - Bob Shurtz (LEGEND) - is the coach of the US Physics Olympiad team and is well plugged in in these matters, but had never heard of this camp.  Considering it has been around since Sputnik, this surprised me.  Further, there were kids from all over the world - India, Hungary and China in addition to the US.  Oh well.  In my next lifetime...

Yeah, that says 104F

Oh yeah... it was HOT.

Also worth checking out - the students at SSP have a blog.  Good stuff.  Watch these kids - they are a bright crew.  And, with any luck, I interested one of two of them in theoretical biology!

Great experience as a lecturer, looks amazing as a student.  Spread the word.

The pre-metastatic niche is only half of the story of metastasis (it's the biological one)

Recently, Cancer Research UK posted an article on their blog in which they explain, in layman's terms, recent trends and ideas in research into metastatic spread. The focus of that article is on the concept of a 'pre-metastatic niche', the idea that the primary tumour emits signalling molecules that prime certain organs for the arrival of metastatic cells. We find this line of thought very interesting, as it could, at least in part, explain patterns of metastatic spread, but have strong opinions about how the ideas were presented and the lack of acknowledgment of the other factors that could be at play.  

First, the reader is given a condensed historical background, in which the surgeon Stephen Paget is given credit for having solved the riddle of metastatic patterns 150 years ago. His method of studying metastatic spread in breast cancer is briefly mentioned, however, as is often the case when the seed-soil hypothesis is mentioned, these old 'truths' do not seem to be carefully checked. For example, a much more recent study from by Dr. J Pickren (reported in The Principles of Metastasis by L. Weiss, p. 231, recently reviewed here), which reports a 4:1 ratio between splenic and hepatic metastases (compared to the 14:1 ratio that Paget observed). Another fact not accounted for by Paget in his analysis, is that the liver not only receives arterial blood, but also blood from the gut organs via the portal vein, thereby increasing the chance of it receiving circulating tumour cells (CTCs). If micro-metasases are present in the gut, then these secondary CTCs will most likely lodge in the liver increasing the risk of developing liver metastases. Lastly, Paget only studied a single location of primary tumours, making general conclusions difficult to draw - especially as the connectivity differs greatly between organs. These simple observations should make it clear that Paget's hypothesis is nothing more than an indication of what might be the case in certain circumstances, rather than a settled fact.

From reading the article one also gets the impression that CTCs are drawn to certain organs in the body (e.g. the caption of the 2nd figure reading "Tumour cells are selective about where they end up." or later in text "...which wandering tumour cells find irresistible."). This is not in agreement with what we know today (and have known for the last 30 years) about the dynamics of metastasis formation.

Figure 1: Human vascular system network topology schematic. It is evident by inspection of the network diagram that tumors originating in the gut and lung experience significantly different flow patterns and order in which they experience filtration at capillary beds than tumors originating in other parts of the ‘body’. The alternate pathways (purple) define the fraction of cells which evade arrest (filtration) at a given capillary bed. There are scant measurements of this in the literature, and none for clinical studies.

On the contrary CTCs have little influence over where they end up, instead the correct picture is that of a primary tumour releasing astronomical numbers of CTCs into the blood stream (roughly 100 million cells per day, of which most die in the blood stream), and that these cells are distributed according to physiology of the circulatory system. 

This means that each organ (except the lung and liver) receive a fraction of CTCs in direct relation to their relative blood supply, and only at this point, at which the cancer cells flow through the capillary bed of the organ, can organ specific mechanisms influence the fate of the cancer cell. This means that any explanation of why patterns of metastatic spread look as they do needs to first take into account the characteristics of the circulatory system, and only then the organ specific mechanisms such as the formation of a pre-metastatic niche.

These facts suggest (at least to us) that one should view the formation of the pre metastatic niche from a more passive point of view. The signals secreted by the primary tumour induce a systemic inflammatory response - which may or may not effect all organs. The evidence suggests that some distant sites respond in a way that makes them more hospitable to the CTCs that happen to pass though them and hence these cells are more likely to form overt metastases - but to present this as an active process is to stretch the data and to anthropomorphize to a dangerous extent.

When attempting to synthesize and communicate difficult scientific information to the public, it is always tempting to present a small slice of the story - and indeed, this is good practice as only so much can be communicated effectively at one time.  But when doing this, it is essential to point out where the limits of our understanding are, and not oversell current hypotheses as the 'truth'.  Science is, and always has been, a steady progression toward understanding, paved by models that are (we hope) less and less wrong.  The way we think today is not likely to be the same as the way we think in 10 years time.

Metastasis - an overview and network perspective

My collaborators, +Philip Gerlee +David Basanta and +Alexander Anderson and I have been working on the problem of metastasis for a few years now, using a physical sciences, network based perspective to try to uncover some truths about this enigmatic process.

Metastatic disease has always been an interest of mine clinically for a number of reasons.  First, metastatic disease causes 90% of cancer death, and the vast majority of morbidity.  Second, for the most part (with a FEW counter examples like testicular cancer and some subsets of limited metastatic disease) we can't cure these patients.  Finally, radiation therapy - my specialty - is extremely well suited to help palliate patients with metastatic disease, and it is very gratifying to help patients in this way.

My scientific interest in metastasis started when I heard about the new technologies for measuring circulating tumor cells (CTCs). I realized that if we could have information about the concentration of these cells at different points in the vascular network at different times, we could infer quite a bit of information about what was happening to them in the organs: something that is currently really hard (impossible) to study in humans.  I drew a hand sketched drawing:

incomprehensible and ugly

and then worked with a medical illustrator in Peter Kuhn's lab named Katya Kadyshevskaya and we produced this: (moral of the story, work with a medical illustrator!)

beautiful and instructive

We published a version of this figure along with a short perspective piece in Nature Reviews Cancer - in which we posited that one could model the vascular system almost like an electrical circuit, considering the CTC flow like current, and the organs like resistors.  We then began working to use the formalism to learn something, other than to simply illustrate an idea (something that +Artem Kaznatcheev has recently talked about in his blog - see! we're learning from our models!)

What we first used this formalism to do was test the 'self-seeding' hypothesis of Larry Norton et al..  This is an hypothesis, first put into the literature in 2006 in Nature Medicine, which suggests that tumors can accelerate their growth by putting cells (CTCs) into the vasculature, letting them circulate around, and then come back to the primary.  This theoretical work was followed by a beautiful experimental paper in Cell, which showed that this phenomenon indeed was occurring, at least in mice. After lots of discussion, we couldn't agree about one of the conclusions of this work - that this mechanism (self-seeding from the primary directly back to itself) could truly drive primary tumor progression, so we built a model to test it.  You can see the full model in this pre-print on the arXiv, or, if you have access, in the Journal of the Royal Society Interface.  I also just presented a poster which summarizes both of the papers I just talked about, and put it on slideshare as an experiment:

Selfseedposter mss2013 from University of Oxford, Moffitt Cancer Center

In short, we find that it is far more likely that there is an intermediate step in between shedding and re-seeding where cells colonize a secondary tissue and subsequently shed their own progeny into the vasculature.  This adds a number of levels of complication and also opportunities for evolution in a foreign landscape - possibly speeding the 'search' for resistant phenotypes (a question I am eager to work on with +Steffen Schaper and +Daniel Nichol).

The next step we are working on (which should be on the arXiv soon) is to show that all metastatic patterns are able to be explained with this formalism, and further, that it represents a novel opportunity to personalized medicine - details to follow!

I've also just finished writing a short review of mathematical models of metastasis.  There has surprisingly little work done in this field and it represents a ripe area for theory.  This review should be available in a book published by Springer later this year, and you can read the pre-print on the arXiv here.  Springer is very open about the policy for pre-prints, which you can read here.  They basically say you can put up whatever you like, pre-acceptance/typesetting/copy editing, and they only reserve the rights to the version that they help with, which makes complete sense.  Seems this publisher is on board with #openaccess science.  Thank goodness.

I should also mention that my collaborator, +Philip Gerlee - wrote a nice post on metastasis a few days ago on his blog and he just promised me another post on it.  Keep your eyes peeled.

New on the arXiv: Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation

I was just trolling the q-bio submissions on the arXiv and came across this new article.  We've made several attempts to include the immune system in our models to date at #IMO, but it isn't easy!  I look forward to reading this one. 

Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation

Kathleen P. Wilkie, Philip Hahnfeldt

Comments: 24 pages, 2 tables, 5 figures, 2 appendices

Subjects: Cell Behavior (q-bio.CB); Tissues and Organs (q-bio.TO)

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development and cancer dormancy. To study this biological phenomenon theoretically we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows us to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict immunomodulation of tumor growth may offer a template for the design of novel treatment approaches that exploit immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.