Axelrod et al: Evolution of cooperation among tumor cells

R. Axelrod, D. Axelrod and K. Pienta: Evolution of cooperation among tumor cells. PNAS vol 103, 36, pp. 13474-13479, 2006.

A few months ago a friend of mine from Vienna send me the link to this paper (thanks Peter!) and although I skimmed through it at the time only now did I have the chance to read it with a little bit more of care. Robert Axelrod is well known in the complex systems and game theory communities. The research he did almost a quarter of century ago (detailed in his book: The evolution of cooperation) explained how cooperation can be established between two agents (people, elephants or cells) even when the mechanisms of the cooperation have not been agreed beforehand and the agents could gain more in the short term by not cooperating.

Now Axelrod and coauthors speculate on how this approach could be used to study carcinogenesis. They present this in the framework of Hanahan and Weinberg and the six capabilities required to progress towards cancer (self sufficiency in growth signals, ignoring anti growth signals, evasion of apoptosis, angiogenesis, limitless replicative potential and invasion/metastasis).

Now, this paper is no regular paper. Most research papers I read describe a particular piece of clinical research (we have investigated this gene in this context...), mathematical or computational model (in this paper we introduce a model that explains the influence of acidity in...) or are review papers. This one does not describe new clinical research nor does propose a formal way to describe any aspect of oncology nor represents a review of carcinogenesis research from the cooperation point of view. This is not meant to be a criticism. The paper represents for me a new category of papers, one whose aim is not as much as telling finished research as to suggest to the reader new venues of research under a particular perspective.

If that was indeed the aim then this is a good paper. According to the authors, the conventional view on tumor progression using the Hanahan and Weinberg framework is that cells have to acquire all the six capabilities but under the new cooperation based view this is no longer necessary. It could be possible that, at least some of this capabilities are provided by some cells to others and thus cancer could occur when groups of cells displaying a mixed set of capabilities collaborate to create the same effect of a single cell acquiring all the capabilities and reaching fixation (taking over the tumour population) by clonal expansion. One of the things that I was not very comfortable with is that the authors state that cancers are the result of genetic (or epigenetic) instability. Readers of this site probably know that this is currently a hotly debated topic (something as fundamental such as: what starts carcinogenesis) and that in front of the Weinberg school (cancer starts from genetic instability) is the , say, Tomlison school (a bigger number of cells and selection suffices to explain the start of cancer). My view is that if tumour cells can cooperate in order to share capabilities and progress down the path of carcinogenesis then having a higher mutation rate might not be so relevant and thus a cooperation based view on cancer would favour the view that cancer does not really need genetic instability to get started. If this view of mine turns out to be a stupidity remember that you read it here first.

The paper provides a number of examples of capabilities in which cooperation can happen. In angiogenesis (where cells can produce growth factors that benefit not only the producing cell but others in the neighbourhood), self sufficiency from (certain) growth signals (there is a certain amount of growth signals which can be produced in paracrine or autocrine fashion) and in invasion/metastasis (collaboration to degrade the ExtraCellular Matrix).

The authors point out that this view of carcinogenesis arises a number of new research questions such as what are the resources that can be shared among cooperating tumour cells, what mechanisms are used to share these resources, how does this affect the order in which mutations appear (since mutations can appear in parallel)? Interesting questions but it might take some for someone to come with the answers...if it is that answers can be found using evolutionary cooperation.

Spencer et al: Modeling Somatic Evolution in Tumorigenesis

S. Spencer, R. Gerety, K. Pienta and S. Forrest. Modeling Somatic Evolution in Tumourigenesis. PLoS Computational Biology, Vol 8, 2, pp 939-947.

Because the paper has been published in an open source journal it means that any reader, regardless of location or affiliation, will be able to download and print it.

I am spending the remaining of this month and most of February in Lyon working with Dr. Benjamin Ribba, from the University Hospital of the University of Lyon. The month will be busy so I am not sure of how much time will be left for posts in this blog but at least on my way here I had time to take a look at the paper mentioned at the beginning.

This paper, together with the one mentioned in a previous post from Anderson et al, tries to create a mathematical framework in which to study the phenotypical view of carcinogenesis presented by Hanahan and Weinberg in their paper. As in Anderson's case, they use a Cellular Automata in which tumour cells occupy the discretised space and can grow and produce angiogenic factors in order to provision themselves with oxygen. The CA is let to evolve the initial population of cells in which mutations might alter the phenotype and acquire any of the six capabilities (ignoring antigrowth signals, production of paracrine growth signals, limitless replicative potential, evasion of apoptosis, angiogenesis and invasion/metastasis). Additionally a tumour cell might acquire genetical instability which significantly increases the mutation rate during mitosis. Cancer is assumed to take place whenever the cells grow over the natural boundaries of the tissue and claim 90% of the total space. This definition of cancer is, at least from my not so extensive experience, quite unconventional since it seems to allow no role to the phenotypes present in the tumour or the the shape of the tumour. At any rate, tumour growth is determined by the ability of the tumour cells of proliferating AND of surviving.

With this not too complicated system, the authors use several simulations to explore different tumourigenetic paths (or as they call them, pathways to cancer). This is how early mutations determine the likelihood of other mutations to appear successfully (the mutant cell has to survive and have other successful offspring) and how some mutations lead to early or later cancer (which I translate as the speed of the tumourigenesis).

So what do they find? They find that the mutator phenotype should play an important role in the case of early onset tumours but not necessarily in others that take more time to develop. They also find that not all the 'pathways to cancer' are equally probable and that is on its own something quite interesting. If in a particular tumour it was possible to see what genes are responsible for particular capabilities in the Hanahan&Weinberg description, then a genetic analysis of representative cells in the tumour could be used to see what further mutations would be the more likely to be successful and maybe design a therapy for it or try to alter the microenvironment to favour other competing mutations.

They also study the heterogeneity of the tumours which is an important feature when designing a therapy. They use a metric based on what it is done in evolutionary biology. The diversity is measured by aligning the different mutational paths of the different cells in the tumour and counting all the ones that have a different path. This seems to me a strange approach given that they treat tumour cells at the phenotypic level. I wonder if it would be better just to count the different phenotypes (defining phenotype in this case as a particular combination of H&W capabilities, regardless of what was the path to reach them)?

To conclude this review: it is clearly a theoretical model aimed to provide qualitative, not quantitative, results. It is probably complicated enough that biomathematicians might not feel very comfortable with it. The results are mainly simulations and it is unlikely that physicians could devise experiments to compare results with the model. Still I have to say that I like it, the quantitative results are interesting enough and the implementation of the word-model is very easy to follow.

Merlo et al: Cancer as an evolutionary and ecological process.

L. Merlo, J. Pepper, B. Reid and C. Maley. Cancer as an evolutionary and ecological process. Nature reviews cancer, Vol 6, pp 924-935, December 2006.

New year and (maybe not so) old traditions: the review of a paper. Nature reviews cancer is one of the world's top scientific journal in terms of impact factor for a reason: they publish very interesting and comprehensive reviews in a field of such importance and as crowded as cancer research. Review papers are comparatively more likely to be cited than the ones about one group's research, review papers in cancer research are normally highly cited since there are so many researchers working in the field. Review papers in a prestigious journal like Nature reviews cancer are thus bound to be cited once and once again and one would expect that only very good scientists would be invited to write for them (I believe that is only by invitation that you get to publish in these journals).

This review covers a topic that is very close to my interests: cancer from an evolutionary and ecological point of view. This view sees a neoplasm, a tumour, as a population of cells with a diversity of inheritable features. This means that evolution will happen and the fitter phenotypes will tend to be more abundant in the tumour population. Questions that might arise are how to alter the mutation rates, clone expansion and how does this expansion happen. Furthermore, given that in many cancers we can find mutations in vast areas of DNA, how do these cells retain enough genetic material to even function? The authors put forward the idea that this could be because most of the human genome is devoted to the development and homeostasis of a multicellular body and thus has no effect on the survival of the single cell in a tumour.

Having a diverse range of individuals whose uniqueness is inheritable is only one of the requirements of evolution. The other one is selection. In a tumour we have two sources of selection. Natural selection is the one that takes place in any tumour when there is scarcity of resources (oxygen, glucose, space). Under these circumstances some phenotypes are bound to be better at surviving and dividing than others. Additionally there is artificial selection which is the result of a therapy applied to a patient with a tumour. Artificial selection changes the fitness landscape, hopefully in such a way as to make survival impossible to every tumour cell. Unfortunately that is somewhat difficult so in many situations is worth altering the fitness landscape in ways that promote the survival of the least aggressive (that is, less likely to be able to invade and metastasise) tumour cells. In any case, altering the fitness landscape in favour of the patient is significantly easier when the tumour did not have much time to evolve.

Evolution in a tumour is not entirely the same as the one in organismal populations. That is to be expected given that tumour evolution lacks something of great importance: time. That is why during chemotherapy, surviving tumour cells are not the ones that develop mechanisms to resist but the ones that due to other reasons (genetic drift for example) already had the capability to resist before the therapy was used. Other differences include the reliance on stem cells for population diversity or that reproduction is asexual (which, incidentally, makes mathematical treatment much easier).

If a tumour resembles an ecosystem we should expect things such as cooperation, competition or parasitism. It seems that you get some of that. Like in an ecosystem individuals compete for the available resources (there is some speculation about that in the paper from Tomlinson reviewed the 10th of October of last year). There are predators if we understand as predation the behaviour of the cells from the immune system when they meet tumour cells. There should be parasitism, mutualism and commensalism (although the authors provide no evidence for that).

I found this a very nice and readable paper. I think it will make a good introduction to any cancer researcher that wants to study the evolutionary aspects of it. My only criticism of a paper that claims to deal with cancer as an evolutionary and ecological process is that the ecological part is significantly weaker than the evolutionary one.

Gatenby and Smallbone: Glycolysis and tumour invasion. Two papers

Why do cancers have high aerobic glycolysis? R Gatenby, R. Gillies. Nature reviews cancer, Vol. 4, November 2004, pp 891-899.

The role of acidity in solid tumour growth and invasion. K. Smallbone, D. Gavaghan, R. Gatenby and P. Maini. Journal of Theoretical Biology 235 (2005) pp 476-484.

Gatenby and Gillies present a review paper in which they explain that the glycolytic metabolism is a requirement for a tumour to progress into a cancer. Cancer cells tend, at least by the time they become invasive, to have an altered glucose metabolism. This metabolism has drawbacks when compared with the conventional glucose metabolism in at least two senses. First of all the glycolytic metabolism is less efficient since it produces 2 ATP (the cell's energy currency) compared with 38 ATP that result from normal metabolism. Second of all, as a by product of this metabolism lactic acid is produced. Lactic acid increases the pH of the microenvironment of the cell and when it reaches a given threshold results in apoptosis or necrosis. As a consequence of this the switch from conventional to glycolytic metabolism does not happen under normal circumstances but under hypoxia, that is, when there is insufficient access to oxygen. In those circumstances the inefficient glycolytic metabolism, which does not need oxygen, represents a significant advantage. Hypoxia is a normal event in a growing tumour since there will always come a point in which the tumour cells are far from blood vessels carrying the needed oxygen. Periodic moments of hypoxia select for cells with the glycolytic metabolism that have adapted to acid environments by, for instance, resistance to apoptosis or by reducing intracellular acidity by pumping it out. The end result of this selection is that a tumour will have a group of cells that, despite having a less efficient metabolism, are capable of harming other cells and also of degrading the ECM (Extra Cellular Matrix, that hold tissue cells together) so the next thing you know is that your tumour cells are capable of invasion and metastasis.

In the second paper, Smallbone and colleagues introduce a mathematical model to study the possibility that tumour invasion and growth could be the result, not of genetic changes, but of changes in the tumour environment. This is, of course, a mathematical formalisation of the hypothesis presented in the other paper. They decided to take multicellular spheroids and produce an ODE model that describes tumour growth and progression as travelling waves: the one for the increased microenvironmental acidity and the second one with the tumour cells invading normal tissue. This is a clearly a quantitative model that, unfortunately, has not yet been validated by in vitro experiments although it looks to me that its design has been done with care so it would be feasible to do so. The model predicts among other things that avascular tumours will have higher acidity than vascular ones (which makes sense since blood vessels can be used to take part of this acidity out of the microenvironment) and that tumour necrosis could potentially be explained without the need to talk about cell starvation or overcrowding but by the acidification of the environment. They make a good case for antiangiogenic therapies since blood vessels can contribute to a decrease of microenvironment acidity that could be sufficient for tumour cells to survive but not for healthy cells that have a lower threshold of acidity resistance. They also suggest a treatment in which the membrane pumps that transport the acidity from within the cell to the outside environment, would be somehow blocked so glycolytic cells would literally poison themselves to death without changing the microenvironment for the healthy tissue cells.

Anderson et al: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment

A. Anderson, A. Weaver, P. Cummings and V. Quaranta. Tumor morphology and phenotypics evolution driven by selective pressure from the microenvironment. Cell 127, 905-915, December 2006.

This is the paper I mentioned in my previous post. It is not that usual to find a mathematical model in a journal like Cell so I hope that this is part of a growing trend.

The paper investigates how the microenvironments helps to drive cancer evolution. To do so they use a hybrid cellular automata model in which cells live in the discrete lattice and the microenvironment (oxygen concentration, extra cellular matrix macromolecule concentration and matrix degrading enzyme) is modeled using continuous variables. The cells are characterised by a number of parameters that determine their behaviour with respect to proliferation, cell-cell adhesion, oxygen consumption, haptotaxis or production of matrix degradation enzymes. Cells follow a life cycle and only proliferate when they reach a certain age. That age depends on the cell's phenotype. During mitosis a cell might alter its phenotype and change the values of proliferation, adhesion, oxygen consumption, etc.

With heterogeneous microenvironment and cell behaviour you get different patterns of tumour growth, some of them favouring agressive invading phenotypes and some of them favouring the coexistance of all sorts of phenotypes. Having the model they described it is possible to study who different microenvironmental factors determine evolution. The results show that harsh environments (little oxygen) select for aggressive phenotypes whereas in milder environments allow for the coexistance of a much bigger range of phenotypes and that these tumours are unlikely to be invasive.

The model is very interesting and the conclusions seem pretty reasonable: Tough microenvironments lead to aggressive tumours. My intuition tells me that on the other hand, heterogeneous populations are more likely to be able to cope with an external aggression which would imply that a less aggressive but more diverse tumour would not respond well to therapies that target any specific kind of behaviour. The main problem with the paper is that the model is fairly complicated for clinical validation.

Bach et al: An evolutionary-game model of tumour-cell interactions

L.A. Bach, S.M. Bentzen, J. Alsner and F.B. Christiansen. An evolutionary-game model of tumour-cell interactions: possible relevance to gene therapy. European Journal of Cancer 27 (2001) 2116-2120.

Bach et al have taken the work from Tomlinson and Bodmer (which I reviewed a few day ago) in which angiogenesis is studied with the help a Game Theory. In the previous case the game involved two players who could chose to produce angiogenic factors or to do nothing. As long as one of the players is willing to shoulder on the cost of producing the factor, both players get the benefit. As expected the result is a polymorphism in which both types of strategies coexist. I said that this polymorphism is to be expected since if there were only factor producing cells then non cooperating cells will have an advantage (since they get the benefits without paying the costs) whereas if the population is made of non cooperating cells then factor producing cells will have an advantage (as long as the benefit of producing the factor is higher than the cost).

The revision of the model proposed by Bach et al considers the implications of extending the game to three players if the benefits of angiogenesis appear only if two out of the three players cooperate to produce the factor.

The payoff table would look like this:

A+,A+ A+,A- A-, A-
A+ 1-i+j 1-i+j 1-i
A- 1+j 1+j 1

where A+ means factor producing and A- means that is not factor producing. Also i is the cost of producing the factor and j is the benefit.

Bach et al analyse how these cost and benefit parameters affect the equilibria and the existence of polymorphism. For this they use computer simulations and find that when the benefit is three times the cost something interesting happens. In that case the final composition of the tumour population would be a consequence of the composition of the original population. Most likely this finding has limited (if any) consequences in potential therapies since physicians have not got the ability to change the initial composition of phenotypes in a tumour. Still, the (qualitative) results can be used as a guide for gene therapies.

Tomlinson and Bodmer: Modelling the consequences of interactions between tumour cells

I.P.M. Tomlinson and W.F. Bodmer. British Journal of Cancer 75 (2) 157-160, 1997.

Again Tomlinson, this time working with Bodmer, taking a couple of simple but interesting examples of the use of game theory for cancer research. This time they work on two different games: angiogenesis and apoptosis. In the first game angiogenic factors might be produced by tumour cells with the result that the cell producing and its neighbours reap the benefits of increased access to nutrients. In the second game cells might produce factors to escape angiogenesis which might or might not benefit the neighbours.

As it is usual in these cases the model assumes a large population of tumour cells, asexual reproduction and a population site that does not need to be constant since the object of the study is the frequency of particular phenotypes, not their absolute number. Further assumptions: the population of tumour cells is genetically diverse and this diversity is distributed homogeneously.

In the first game: angiogenesis, there are two strategies: either to produce or not to produce angiogenic factors. There is a cost associated to producing then and also a payoff. If you are a non producing tumour cell and you interact with a producing tumour cell you get the same benefits but none of the costs of a factor producing tumour cell. The result is that there are equilibria in which both phenotypes coexist as long as the cost of producing angiogenic factors is outweighed by the benefit.

The second game is more sophisticated. In this case we have three different strategies: either we produce factors to help neighbouring cells avoid apoptosis (paracrine factors), or we produce autocrine factors that help us avoid apoptosis or, alternatively, we might save ourselves all that trouble and do nothing. As usual there is a payoff table in which the different parameters represent the costs of producing paracrine and autocrine factors and the benefits they provide to whoever is the target of the factor. Tomlinson and Bodmer use GT to study different types of equilibria.

In this case it is easy to see that the first strategy is not viable since any group of cells doing nothing and reaping the benefits of endocrine factor producing cells would drive them to extintion. On the other hand if the cost of producing autocrine factors is smaller than the benefit of avoiding apoptosis then there will be a selection for cells capable of producing those autocrine factors.

The conclusion of the paper is that a tumour cell population might not adopt a strategy that would help the whole but does not confer any advantage to the individual that brings it (which is a reasonably safe proposition to make to people studying evolution). The question is again if there could be therapies designed to exploit the fact that tumour cells can stop cooperating among each other.

I.P.M. Tomlinson: Game theory models of interactions between tumour cells

Review of EJC 35-9 (1997) 1495-1500.

This is the first paper I am aware of that uses game theory to study a problem in the field of cancer research. The paper is only from 1997 so it is easy to see that the field is ripe for further development.

The advantage of being the first to use a given tool in any area is that you can chose the problem and come with an simple and elegant study. Tomlinson has used a simple system in which tumour cells can adopt a number of strategies such as producing cytotoxic substances and cytotoxic resistance. The hypothesis is that some tumour cells attempt to gain advantage by actively harming neighbouring cells. This initial hypothesis is studied considering a number of different scenarios in which different phenotypes are combined. Initially there are three types of phenotypes or strategies: cells that can produce cytotoxic substances, cells that can produce factors that protect them from cytotoxic substances and finally cells that do none of this. Tomlinson presents a payoff table in which the interactions between the different phenotypes are presented in a parametrised way so he can hypothesise different values of the cost it represents to produce the toxin or the cost of producing the resistance or the benefit conferred to harm a player by doing so. Once the game is properly defined he goes on to study the potential equilibria by running simulations on a computer and varying the different parameters of the payoff table.

He also studies alternative strategies such as phenotypes that produce both the cytotoxic substance and its resistance and flexible strategies that behave differently according to the phenotype of the player they compete against. The conclusions he obtains are that several phenotypes can coexist simultaneously in a tumour (since there are configurations of parameters of the payoff table that lead to equilibrium), that flexible strategies are better than fixed ones (unless the cost of flexibility is too high and that therapies could be designed that could exploit the fact that tumour cells can harm other tumour cells under some circumstances (maybe promoting competition and not collaboration among them).

Of course the model is very very simple and the conclusions should be taken with some care (there are no spacial considerations, no hints of what the parameters of the payoff table could be, the results are not surprising). Still, this model gives some theoretical backing to these conclusions and suggests some ideas on how to design a therapy which is quite nice.

Mansury, Diggory and Deisboeck: Evolutionary game theory in an agent based brain tumor model: exploring the 'genotype-phernotype' link

Mansury et al. JTB 238 (2006) 146-156.

One of the things I had in mind when I started this blog is that I could use it to force me to write reviews about some of the most relevant papers that I often read for my own 'dirty' purposes. Usual reasons apply: it is good to write about what you read since synthesis helps understanding.

In any case, as you know, one of the topics I am interested on is cancer research using evolutionary game theory and although evolution is not what these people have studied the other important keywords are present in this paper.

Mansury et al have devised a nice spatial (2D lattice) agent based (Cellular Automata style) system in which tumour cells inhabit a space with nutrients. Tumour cells can be found in two varieties: A (proliferative) and B (migratory). Non evolutionary game theory is used to analyse the interactions between cells that have different phenotypes and how those interactions reflect on the payoffs of the individual cells and on the tumour as a whole. The payoffs in this game are slightly more complicated (and according to the authors, more realistic) than those of other games. The payoff of a cells is made of three different factors: communication payoff, proliferation payoff and migration payoff.

For the simulations (since it is quite difficult to come with a nice analytical study) they run CAs with 500x500 lattices in which nutrients are diffused from the centre and the middle. From here they study how changing the payoff table results in different velocity of tumour growth, different tumour surface roughness (useful to analyse the malignancy of a tumour) and the numbers of both tumour populations with time

From my point of view, the most significant shortcoming of an otherwise interesting piece of research (and acknowledged by the authors) is the lack of evolution in the model. With evolution out of the equation the condition under which phenotypes emerge and take over the original population cannot be studied. One of the nice features of game theory is that it can be used to study the equilibrium states of tumour cell populations when those tumours are studied as composed of individual cells (or agents in Mansury's et al model). Since the author's know this I am looking forward their next paper to see how the improved model can be used to study carcinogenesis.