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.

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:

http://www.biorxiv.org/content/early/2014/08/03/007542

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!

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.

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.

Cancer is a sine qua non for life as we know it.

There was a post today on National Geographic talking about a tumor that was found in a fossilized Neandertal's bone. It reminded me that I had written the piece below and hadn't found a home for it yet. The title, which is a big jarring, is:

Cancer is not a disease: there is no cure.

The way we describe things shapes and is shaped by the way that we think of them.  Cancer has been described as a disease for as long as we have written record of medicine.  It’s name comes from the greek word for crab, because the way it wedges itself into the host tissue is so like a crab wedges itself between rocks: inextricably.  

The advent of the microscopic age at the turn of the 20th century brought with it an unprecedented view of the cellular level; anatomy and pathologies came into a new focus and a new science was born: microbiology.  As physicians, we were offered a new opportunity to study diseases at the cellular level, to describe the panoply of new patterns that we saw under the microscope much like a team of explorers coming into undiscovered jungle filled with undescribed flora and fauna.  We found that the cancers in each organ were not necessarily the same.  Indeed, we found a rich diversity of cancers that could be reliably classified and whose prognoses and patterns of progression correlated.  This richness of classification gave rise to the opportunity for disease specific treatment trials, and indeed accounted for most of our progress against these individual entities, and for the standard of care for most cancer types even today.  

The dawn of the genomic age, first with the human genome project, and then with the cancer genome atlas, promised and delivered another wave of discovery and deeper, more detailed classification.  Just as we can now tell how, and when two species of finch, or cave fish, diverged in their evolutionary history, so too can we tell when and how a tumor diverged from its tissue of origin.  Early on in this story, we were tantalized by the discovery of specific genomic errors (mutations) that seemed to explain a cancer’s growth, and with the discovery of imatinib, a targeted ‘cure’ for a specific cancer (CML), and cancer seemed to be on its knees, ready to be cured.  

The final cure, however, has continued to elude us.  As we continue to discover more and more specific mutations, drug companies continue to develop specific drugs to target their action.  Each of these drugs seems to work well in a subset of patients, for a time, but never provides the silver bullet that we have been promised, and ultimately fails in almost every case.  The problem is that we are stuck in a paradigm where each disease has a cause, and each cause has a remedy.  This linear thinking has dominated medicine, and indeed much of science, for most of human history, and has served us well.  But continuing to think of cancer as a disease in this paradigm is not going to get us any closer to a cure - we have to shift our thinking and expectations, and embrace the reality that cancer is the result of a non-linear, highly degenerate process, and therefore has no 'cure'.

We have to shift our focus in the study of the cancer genome and stop trying to develop a comprehensive list of errors in the code that cause cancer, but instead learn the guiding principles behind the process - the equations of motion, if you will.  Cancer is not a disease to be cured, but a pathologic condition of normal tissue evolving according to the very rules which allowed us to emerge from the primordial ooze.  It is an inconvenient sine qua non for existence in our universe, as evolving, living organisms.  

This reclassification is not intended to take anything away from those living with cancer, or who have suffered from it.  Within any single patient, this pathologic condition has the capacity to cause as much, or more, suffering than does any other disease.  And, as oncologists, our calling is to minimize this suffering, and when we can, cure our patient.  But until we stop thinking about cancer as a disease that is the product of a linear process, and realize that it is a pathologic condition that is produced by any number of trajectories across an evolutionary landscape; until we stop looking for a single, silver bullet cure for all patients that doesn’t exist, we will continue to waste time that we could be using to understand the evolutionary dynamics of cancer so we can develop strategies to cure each patient.


Some further reading:

Exploiting ecological principles to better understand cancer progression and treatment
arXiv preprint
Basanta and Anderson

Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective.

Huang et al. Semin Cell Dev Biol. 2009 Sep;20(7):869-76. doi: 10.1016/j.semcdb.2009.07.003

Oxidants, antioxidants and the current incurability of metastatic cancers.

Jim Watson, Open Biol. 2013 Jan 8;3(1):120144. doi: 10.1098/rsob.120144.

Cool "snake" I saw the other night and convergent evolution

So around 7pm the other night I was taking a walk with my wife and baby boy (we live in Tampa, FL) and we saw this cool snake:

It was quite docile and never struck at the stick I poked it with.  It didn't move very efficiently, not much of a slither, more of a thrashing around kind of movement.  It's belly was yellow and smooth, and it had a funny tip to its tail.

Now, I quite like snakes.  My mom signed me up for NOAH (the northern Ohio association of herpitologists) when I was 10, and she and I went to all the meetings and I got to visit some labs of herpitologists at the local universities.  After about a year, she let me get a red-tailed boa (who I named Rocky, as in Rocky BalBOA).  This snake was awesome - my mom used to vacuum with it around her neck, and it cuddled with our golden retriever, Casey.  No Joke.  We eventually got a California kingsnake (Damian) as well, but it wasn't as friendly.  Anyways, I digress.  The point is, I like snakes, so I was curious about this one, that I didn't recognize, in my own neighborhood.

So I looked at this nice website called Florida Backyard Snakes.  And, I got bupkis.

So I crowd-sourced the ID to twitter, and within 20 minutes, was told by two users (thank you @LinkLayer and @GaryBurness) that it wasn't a snake at all, but a legless lizard! (The Eastern Glass Lizard, Ophisaurus ventralis to be precise) So, there's the nature lesson for the weekend.  Not a cancer related one, but fun nonetheless.  But, if I stretch, I could say this post is really about convergent evolution, something which many cancer cells experience as they "find" the invasive/metastatic/glycolytic phenotype.  There, cancer connection.  Done!

Also, how awesome is my mom?  

Happy Mother's Day Momma, thanks for instilling a life long curiosity into this boy - I'll pay you back by doing the same for my kiddos.