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.

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.

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.

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.

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.

The case for pre-prints in biology

So when I first met +Jonathan Eisen at TEDMED in 2012, in addition to the social media mandate he gave to me, he started to introduce me to the whole #openaccess debate (his brother founded PLoS and he is the chair of the advisory board at PLoS Biology).  As a physicist by training, I was an easy convert, but I've found that MANY of my biological colleagues (even the theoretical ones) have been more difficult to sway.

I just had a conversation today, in our awesome collaboration space - the collaboratorium (this panorama doesn't do it full justice, but there's +Philip Gerlee)

with a friend and colleague Jonathan Wojtkowiak (who doesn't seem to have a G+ account), where I faced the same arguments that I've heard so many times before:

Why should I post my papers on a pre-print server where anyone can see it before it is published!?  They could scoop me!

I honestly don't understand this argument, but I hear it all the time.  By nature of pre-print servers, like the arXiv, the idea is yours! Time and date stamped. And, better yet, it is completely #openaccess, free of charge, and helps move science along at a better pace.  Only a very few journals have problems with posting of pre-prints before they get their (greedy) hands on the results of all your hard work, but most are totally OK with it.

There is a nice movement starting in biology to get things posted.  And some communities, like the population and evolutionary biology one, have their own pre-print discussion site - Haldane's Sieve.  I am starting to consider trying to do something similar for quantitative cancer research as well, with the help of some friends and colleagues, but we'll see.

If you still aren't convinced, here is a nice article in PLoS Biology highlighting the issue.  Also, take a look at the some of the nice press that my mentor +Alexander Anderson and +David Basanta recently got on a pre-print about Game Theory and cancer they posted by MIT Technology Review - this is press this article likely wouldn't have gotten through the standard route... and we know that you don't get cited unless people read your paper...

If you are against it - please leave some comments about why, I'd love to try to convince you otherwise!  If you are a biologist (or know one) who DOES post pre-prints, weigh in and share your good experiences!

New on the arXiv from IMO. Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance

A new paper from +Jill Gallaher and +Alexander Anderson is out on the arXiv.  I asked Jill for a PLoS style 'author summary' in non-technical language, and here it is:

Author Summary:

A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells. A tumor is more of a complex system of many interacting cellular and microenvironmental elements. There is variation among cells within the tumor, and with an increased proliferation capacity, there is competition for space, so evolution and selection occurs.  Because our current understanding at the genetic scale gives little information on translating to actual changes in cell behavior, we bypass the translation of genetics to behavior by focussing on the functional end result of the cell’s traits (phenotype) combined with the environmental influence of limited space, which will ultimately dictate tumor aggressiveness and treatability. 

The evolution of the population depends on the way in which traits are passed on as cells divide. We investigate trait inheritance by building a cell based simulation in which individual cells with varied trait combinations compete for space over time. Specifically, we characterize cell behavior in terms of two traits: proliferation rate and migration speed. The mode in which these traits are inherited significantly affects the evolution, composition, and fitness of a tumor population. To investigate competition for space, we initiate the population as a tight cluster, representing a growing tumor mass, and as a dispersed population, representing a cell culture experiment. We find that the dispersed population has more space, less competition, and reduced selection.  With a growing cluster of cells, there is more competition and selection. But constraining the allowable trait combinations so that several phenotypes are equally fit reduces competition and leads to the coexistence of several phenotypes. In this case, local heterogeneity may be advantageous to maximize growth.

As before, any comments on the paper will be passed directly to the authors!  Here is the link and abstract:

http://arxiv.org/abs/1305.0524

Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance

Jill Gallaher, Alexander R. A. Anderson

(Submitted on 2 May 2013)

A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumor with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cell's capacity to survive and propagate is determined by its combination of traits and interaction with the environment. With heterogeneity in phenotypes, the clone that will dominate is not always obvious as there are both local interactions and global pressures. Several combinations of phenotypes can coexist, changing the fitness of the whole.
To understand some aspects of heterogeneity in a growing tumor we build an off-lattice agent based model consisting of individual cells with assigned trait values for proliferation and migration rates. We represent heterogeneity in these traits with frequency distributions and combinations of traits with density maps. How the distributions change over time is dependent on how traits are passed on to progeny cells, which is our main inquiry. We bypass the translation of genetics to behavior by focussing on the functional end result of inheritance of the phenotype combined with the environmental influence of limited space.

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.

A nice paper from our group (not me) recently posted on the arxiv.  Any comments are most welcome and will be passed directly to the authors.

Here is the link to the pre-print of:

Senescent fibroblasts can drive melanoma initiation and progression

By Eunjung Kim et al.

This is a collaboration between a theory group (Integrated mathematical oncology) and a wet lab (Smalley PI) and a great example of how a collaboration should work between theorists and experimentalists.

http://arxiv.org/abs/1304.1054

Melanoma is the most devastating form of skin cancer arising from the melanocytes, the pigment producing cells of the skin. Its initiation and progression is known to involve genetic changes in melanocytes as well as the disruption of both cell-cell and cell-microenvironment interactions. However, the mechanisms by which the deregulated interactions lead to melanoma development have been less understood. It is our view, that we must first model normal skin form and the regulatory mechanisms that maintain skin homeostasis before we can model cancer initiation. To this end, we developed a hybrid multiscale mathematical model of normal skin (virtual skin). The model focuses on key cellular and microenvironmental variables that regulate normal skin homeostasis. The model recapitulates normal skin structure, and is robust enough to withstand physical as well as biochemical perturbations. Furthermore, the model revealed the important role of the skin microenvironment in melanoma initiation and progression. Experimentally, we found that as fibroblasts, an importance source of growth factors in the skin, become senescent their behavior changes significantly, leading to the expression of multiple growth factors, matrix proteins and proteases. We incorporated senescent fibroblasts into model to examine how microenvironmental changes affect skin structure. Our simulations showed that senescent fibroblasts transform the skin microenvironment and subsequently change the skin architecture by enhancing the growth and invasion of normal melanocytes as well as early stage melanoma cells. These predictions are consistent with our experimental results as well as clinical observations. Our co-culture experiments showed that the senescent fibroblasts promote the growth and invasion of non-tumorigenic melanoma cells. We also observed increased proteolytic activity in stromal fields adjacent to melanoma lesions in human histology. Based on our simulations combined with clinical data, we speculate that senescent fibroblasts may create a pro-oncogenic environment that cooperates with mutations to drive melanoma initiation and progression.

http://arxiv.org/trackback/{1304.1054}

Not all modeling is mathematical!

I found a nice blog from an entomologist at 'a teaching institution' through a post on twitter that raised my hackles a bit. The tweet, and title of the blog post was:

Ant science - how avoiding modeling led to a cool discovery

By this, he meant *mathematical* modeling. In the wake of the whole EO Wilson good scientist=\Good at math post on WSJ (yes, I'll post about that later in detail), I thought this deserved a reply. So, I responded with a comment on his blog, which I will append here. The comment is basically a short summary of a previous post, but it bears repeating, I think.

His post describes how he made a discovery about an species of ant by looking for big picture patterns, and not paying so much attention to the details... Being a Kepler, not a Newton if you will... It is worth a read, as it is well written and interesting, especially if you like ants.  Anyways, here's what I said in return, referencing an earlier post of mine:

*
Hello, and a pleasure to find your blog. I enjoyed this post, and it is fitting as I literally JUST put down EOWs new book 'letters to a young scientist'. Anyways, I'd like to respectfully disagree a bit, and mostly semantically. This is NOT avoidance of modeling. It is just doing a modeling of a different sort. I recently (started and) wrote a blog post about just this issue, specifically in communication between mathematical and experimental biologists - which can be read here:

Whose model is it anyways?

Where I talk about how we are really ALL modelers! Our models just look different. Where the data collecting scientist (think Tycho Brahe) spends his/her time dreaming about where to look and what to look for, the pattern former (your role here - think Johannes Kepler) seeks the big picture patterns and the 'modeler' in your terminology (Isaac Newton in the analogy I've been using) puts together the more rigorous connections. There is no rigorous theory without patterns to connect, and there are no patterns without data. We are all on the same team. And, it's a lot of fun whichever role you play.

Anyways, great post, just wanted to argue the semantics :)

\end{rant}

For full disclosure, I'm a phd student in mathematical biology.
*

For even more full disclosure, I stole the 'we are all modelers' from my mentor +Alexander Anderson - cheers Sandy.  And it turns out that I stole the whole Brahe->Kepler->Newton thing from Lord Robert May's lovely article on mathematical modeling in biology, though I didn't mean to.