cancer and the cell cycle

Last Friday I came to the Max Planck Instute for Cell Biology, at the other side of Dresden, to attend a series of seminars including one from a colleague and friend of mine, Babis Hatzikirou, about the cell cycle.

The classical view on the cell cycle can be seen in this picture that I took from Babis's presentation (and which I suspect he took from somewhere else :)):
This is quite interesting although not precisely research news. Most of the cell cycle is of course devoted to interphase and only a minority of the time (assuming that the cell is not in arrest mode) is devoted to create a copy of itself (through mitosis and cytokinesis). The cell cycle is controlled by a finely tuned balance of proteins cdc2-cdc13 and a number of checkpoints make sure that before changing the phase of the cell cycle everything is in order. These checkpoints and their associated proteins (such as the famous TP53) are quite critical to prevent tumour formation as they impede the growth of cells that need DNA repair.

A 3D model of human breast cancer

This has been covered in a few places like the BBC and ScienceDaily. It seems that some researchers at Queen Mary College in London have recently come with a non animal 3D human breast cancer model.

This is interesting at more than one level. Their research was funded by a research charity (Dr Hadwen Trust) that supports the development of methods that avoid animal experiments. Working with rats is not that satisfactory for ethical reasons and also because there are many cases in which the results of rat experiments cannot be extrapolated to humans (seems we are not so similar in some respects after all). It is also much more realistic than just taking some human cancer cells and studying them on a petri dish.

Being capable of performing experiments using realistic 3D models quickly and efficiently is one of the holy grails of theoreticians since it would make experimental validation of our models much easier (confusingly enough what theoreticians call model, eg, equations or computer rules, is not what experimentalists understand as a model, eg. rat, arabidopsis or drosophila). This validation is quite complicated as I have already mentioned in another post. Making this validation easier and more convenient will go a long way in terms of making our work more reliable and quantitative.

Autophagy and cancer

This is a new cellular mechanism I did not know about: autophagy. Nature's issue of April 12th (I am bit behind I know) has an interesting article in the section Q&A on autophagy and its role in cancer.

Autophagy is the process by which cells degrade faulty or redundant components. It is used by cells when they need to reuse molecules for other uses and also it plays an important role in complementing apoptosis. Both apoptosis and autophagy are connected to cell death but in the case of autophagy cell death is not always the outcome although it can be a substitute when the apoptotic mechanism is crippled. In that case the cell literally eats itself to death.

The image bellow comes from the article. Autophagy has the potential of being useful for cancer supression but also for cancer promotion. The balance is important, too little and you get cell death when the cell cannot produce things it needs by reusing parts of itself. Too much of it and you also get cell death since the cell can eat itself. Altering this balance in a tumour cell could be the source of a new therapy although as usual it is important to remember that cells might evolve mechanisms to avoid the trouble of autophagy, maybe by inactivating the atophagy mechanism all together. Even in that case the tumour cell would be less capable of surviving in situations of stress since it would not be able to recycle material.

Autophagy seems to be a mechanism whose precise role in cancer has not been fully studied yet but could be a promising extra target for a multi target therapy that could hinder cancer evolution and growth.

Mini workshop on cancer and cellular automata

Today we are hosting in our group at TU Dresden a mini workshop on cellular automata in biology. Three talks (one in the morning and two in the afternoon) are actually about CAs and cancer. It will be a busy but interesting day.

The booklet for the afternoon part of the workshop (the longest part of it) is here.

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.