I gave yesterday a small and informal presentation on the research done in cancer using game theory. For whoever might be interested, the results are here.
Month: October 2006
Interview with mathematical biologist Luigi Preziosi
I guess it will be irrelevant for those of you that don’t speak Spanish but the Spanish news paper El Pais has interviewed the mathematical biologist Luigi Preziosi. Luigi happens to be one of the coordinators of the EU Marie Curie Network in which I am involved.
In the interview he argues that biology is geting more mathematical, explains how mathematicians and life scientists and physicians collaborate, how the mathematical models can help to explain medical phenomena and hint to innovative therapies. He also says that traditional biologists are still necessary (as if that was not obvious: theoretical physicists still need experimentalist to work with so they can validate their theories, it should not be different in the life sciences, there would not be biology without people that know how to perform experiments).
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.
Tumour supressor gene involved in virus protection
Got this from mainstream media but the paper itself has been published in the EMBO journal in September. Researchers at the Madrid based Centre for Oncological Research have found a gene (for those interested in the gene itself: ARF) that is implicated in both tumour supression and protection from viral infection.
I guess this amounts to another cellular mechanism that has been successfully evolved to adopt an extra new function. The results of evolution can be messy but I’m still impressed.
Darwin online
Heard it on the radio this morning while listening to the BBC: the University of Cambridge has digitised the text and images of thousands of pages from the publications of Charles Darwin. The website can be found here: http://darwin-online.org.uk/.
Included in the collection are works on other members of the Darwin family (such as the almost-as-famous-as-his-grandson Erasmus Darwin) as well as mp3 audio books for those who would like something more intellectual to entertain their daily jog or gym workout.
Evolution and cancer news
Every morning I check a couple of sites in order to get an overview of what is going on in the world. Today I found a couple of curious things:
On the more serious (and cancer related) front, A group of researchers at the University of Missouri-Columbia have found a way to find out the spread of skin cancer cells through the blood. The technique relies on the fact that the vibrations produced by a laser into a melanoma cell is different from that of other cells like red blood cells and plasma.
More information can be obtained here (for those with a subscription to the journal of optics letters).
A different kind of research has been noticed by the bigger media (BBC, Telegraph) and it seems to illustrate how not to use the theory of evolution. Researchers at the Darwin centre at the London School of Economics have seen the future and came back to tell us: Mankind will split into two separate species: the clever and beautiful and the dim-witted goblin-like. I have already heard people labelling these groups as the Macs and the PCs.
Turning on genes again
I confess to read The Economist newspaper more than occasionally and I find the Science and Technology section readable but rigorous.In this week’s issue there is an article about a new class of drugs that has recently gained approval in the US.
One of the things I have learned reading this article is about how mutations might occur that could lead to tumour formation. Up to now, as far as I was concerned, a mutation is a mutation is a mutation, that is, something that just happens and, ooops, one more ticket for the lottery of cancer. Well, it seems that a curious way to turn off large parts of the DNA is by increasing the packing density of the DNA so it becomes effectively unreadable. It seems that cancer cells can use this mechanism to avoid expressing genes so they can proliferate faster as well as avoid apoptosis and senescence. Given that the drug that has just been granted regulatory approval works best with leukemia it seems that the mechanisms employed by tumour cells to deactivate certain cell mechanisms varies from cancer to cancer. Still, having cancer cells with the capability of turning off significant parts of the DNA is such an evolutionary advantage that it should not be surprising if equivalent mechanisms are found in other types of cancer.
Another article on Richard Dawkins
An interview of Richard Dawkins in Salon. It is possible to read the full article if you click on the sponsor link.
Salon has a series of interviews about science and religion and this time they decided to interview Prof. Dawkins who, they claim, is second to the late Stephen Jay Gould in popularising evolutionary biology (I would claim that here in Europe Dawkins is probably better known).
Usual readers of this blog (hi mum!) know that I am a fan of Prof. Dawkins and share some (if not most) of his ideas about evolution and its lack of compatibility with established religions (the interview, and his new book – The god of delusion – deal mostly with the three big monotheistic religions although touches too any faith-based religion…which I guess means any). Reading this wont give you a new insight on cancer. Moreover, if you are a religious person, it is unlikely that you will be transformed into an unapologetic atheist, but it still makes an interesting read IMHO.
For the record, the book of Richard Dawkins is The god of delusion. For an alternative view from another famous scientist (Stephen Jay Gould, probably second to Dawkins popularising evolutionary biology) take a look at Rock of Ages. His view is that science and religion belong to different realms and should not be intermixed.The links are to wikipedia.
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.
Article in Nature: Driven to Market
Nature has a reputation for publishing academic articles of high-impact (that is, loads of people read nature so articules in nature are widely read and are more likely to be cited by other people which means that Nature becomes better ranked which means that more people buy it which means…), but also they have some nice articles that are more accessible to non specialists and that are written by freelance writers.
Yesterday I was reading one in last week’s (I am always late with my issue) entitled “Driven to Market” by Jonah Lehre. The article is about a relatively new field called neuroeconomics which combines both psychology and economics. That does not seem related to the topic of this blog but what it is interesting (to me) is that one of the assumptions that is prevalent in economics and that the practitioners of neuroeconomics bring to question is that humans act guided by reason in order to maximise their own benefit. This is also one of the main assumptions in Game Theory (which is a common tool in Economics). Ironically one of the criticisms that opponents of evolutionary game theory have is that animals are not rational but it seems that reason is an even weaker predictor of the behaviour of humans. One nice example to illustrate that is the game called ultimatum. In this game one player is given, say, 10 euros and told that it has to share it with someone else in such a way that if any of the players is unhappy with the way the money has been split then no one gets anything. If people were rational the first player will always offer 1 euro to the second one knowing that the second one would take whatever he or she is offered since the alternative is to get nothing at all. It seems though that when this game is played by people, deals that seem to be too unfair are always rejected even if that rejection means that the money is lost.
Cancer Ecology 