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.

University rankings

As long as you don’t take them seriously it is amusing to take a look at university rankings once in a while. This one comes from the The Times Higher Education Supplement.

1 Harvard University
2 Cambridge University
3 Oxford University
4= Massachusetts Institute of Technology
4= Yale University
6 Stanford University
7 California Institute of Technology
8 University of California, Berkeley
9 Imperial College London
10 Princeton University
11 University of Chicago
12 Columbia University
13 Duke University
14 Beijing University
15 Cornell University
16 Australian National University
17 London School of Economics
18 Ecole Normale Supérieure, Paris
19= National University of Singapore
19= Tokyo University
21 McGill University
22 Melbourne University
23 Johns Hopkins University
24 ETH Zurich
25 University College London
26 Pennsylvania University
27 University of Toronto
28 Tsing Hua University
29= Kyoto University
29= University of Michigan
31 University of California, Los Angeles
32 University of Texas at Austin
33= Edinburgh University
33= University of Hong Kong
35= Carnegie Mellon University
35= Sydney University
37 Ecole Polytechnique
38 Monash University
39 Geneva University
40 Manchester University
41 University of New South Wales
42 Northwestern University
43 New York University
44 University of California, San Diego
45 Queensland University
46= Auckland University
46= King’s College London
48= Rochester University
48= Washington University, St Louis
50= University of British Columbia
50= Chinese University of Hong Kong
52 Sciences Po
53 Vanderbilt University
54= Brown University
54= Copenhagen University
56 Emory University
57 Indian Institutes of Technology
58= Heidelberg University
58= Hong Kong University Sci & Technol
60 Case Western Reserve University
61= Dartmouth College
61= Nanyang Technological University
63 Seoul National University
64= Bristol University
64= Ecole Polytech Fédérale de Lausanne
66 Boston University
67 Eindhoven University of Technology
68 Indian Institutes of Management
69 Amsterdam University
70= School of Oriental and African Studies
70= Osaka University
72 Ecole Normale Supérieure, Lyon
73 Warwick University
74 National Autonomous Univ of Mexico
75 Basel University
76 Catholic University of Louvain (French)
77 University of Illinois
78 Trinity College Dublin
79= Otago University
79= University of Wisconsin
81 Glasgow University
82= Macquarie University
82= Technical University Munich
84 Washington University
85 Nottingham University
86 Delft University of Technology
87 Vienna University
88 Pittsburgh University
89 Lausanne University
90= Birmingham University
90= Leiden University
92 Erasmus University Rotterdam
93= Lomonosov Moscow State University
93= Pierre and Marie Curie University
95 Utrecht University
96 Catholic University of Leuven (Flemish)
97 Wageningen University
98 Munich University
99= Queen Mary, University of London
99= Pennsylvania State University
101 University of Southern California
102= Georgetown University
102= Rice University
102= Sheffield University
105= University of Adelaide
105= Humboldt University Berlin
105= Sussex University
108 National Taiwan University
109= St Andrews University
109= Zurich University
111= Maryland University
111= Uppsala University
111= Wake Forest University
111= University of Western Australia
115 University of Twente
116= Fudan University
116= Helsinki University
118 Tokyo Institute of Technology
119 Hebrew University of Jerusalem
120 Keio University
121 Leeds University
122 Lund University
123 University of North Carolina
124= University of Massachusetts Amherst
124= York University
126 Aarhus University
127 Purdue University
128= Kyushu University
128= Nagoya University
130= Tufts University
130= Virginia University
132 Durham University
133= University of Alberta
133= Brussels Free University (Flemish)
133= Hokkaido University
133= Newcastle upon Tyne University
137 Nijmegen University
138 Vienna Technical University
139 Liverpool University
140 Cranfield University
141= University of California, Santa Barbara
141= Cardiff University
141= Ghent University
141= Southampton University
145 Georgia Institute of Technology
146 RMIT University
147= Chalmers University of Technology
147= Tel Aviv University
148 Free University Berlin
150= Korea University
150= Texas A&M University
152 Notre Dame University
153 Bath University
154 City University of Hong Kong
155 McMaster University
156= Curtin University of Technology
156= Göttingen University
158= Technion — Israel Inst of Technology
158= University of Ulm
158= Waseda University
161= Chulalongkorn University
161= University Louis Pasteur Strasbourg
163 Michigan State University
164 Saint Petersburg State University
165= Brussels Free University (French)
165= China University of Sci & Technol
165= State Univ of New York, Stony Brook
168= George Washington University
168= Tohoku University
170= University of California, Davis
170= University of Tubingen
172= Aachen RWT
172= Maastricht University
172= Royal Institute of Technology
172= Yeshiva University
176 Queen’s University
177 Oslo University
178 University of Bern
179 Shanghai Jiao Tong University
180 Nanjing University
181= Kobe University
181= Université de Montréal
183= Jawaharlal Nehru University
183= Free University of Amsterdam
185 University of Kebangsaan Malaysia
186 Innsbruck University
187= Brandeis University
187= Frankfurt University
187= University of Minnesota
190= University of Barcelona
190= Reading University
192= Malaya University
192= Queensland University of Technology
194 Technical University of Denmark
195 Aberdeen University
196 University of Wollongong
197 La Sapienza University, Rome
198= University of California, Irvine
198= Korea Advanced Inst Science & Technol
200 University of Paris-Sorbonne (Paris IV)

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.

Recap from Lyon (II)

Philip Maini is one of the most entertaining speakers (entertaining in the good sense, of course) in the European biomathematical community. Prof. Maini is the director of the Centre of Mathematical Biology at Oxford University and gave in Lyon a talk entitled “Modeling aspects of cancerous tumour dynamics”.

The modeling aspects he mentions are three different projects:

1) The first project, in which he collaborates with people like Gatenby (Arizona) and Gavaghan (Oxford) studies the acid mediated invasion hypothesis.
According to (my interpretation of) this hypothesis, when tumour cells lack oxygen and start to starve then a mutation might appear that would make some cancer cells switch to what is called glycolitic phenotype. This means that these cells have an alternative metabolism that works without oxygen and that is not as efficient as the regular one. The reason why this alternative phenotype has a chance of success is because the waste produced (galatic acid) can be used to degrade the extra cellular matrix and lead to invasion of other tissue. Gatenby, Gavaghan and Maini came with a model in which tumours contain cells with the glycolitic phenotype. The results is that tumours are not benign and that an possible explanation for the existence of necrotic cores (material generated when cells die disorderly because of starvation) can be the result of too much acidification of the environment, even for acid-resistant glycolitic-type tumour cells.

2) Metabolic changes during carcinogenesis. Also with Gavaghan and Gatenby and referring to research covered by a paper in Nature reviews cancer (vol 4, 891-889, 2004). They study somatic evolution in a system in which tumour cells can be of one of three different types: hyperplastic, glycolitic or acid-resistant. These cells inhabit the space of a 2D lattice in which there is oxygen, glucose and hydrogen that diffuse in a continuous manner. Altering the reach and concentration of these elements leads to different numbers of cells displaying one or the other phenotype.

For me this is a good place in which to see how game theory could be used to study the interactions of different players (cancer cells) using different strategies (the different phenotypes) to maximise their payoff from the environment (O,H,glucose).

3) Together with Benjamin Ribba (Lyon, organiser of the workshop and one guy I am working with as of lately) Maini works on a multiscale model on which to study the differences between the vasculature generated by the normal process of vasculogenesis and the ones generated by tumour cells capable of angiogenesis. One of the conclusions he mentioned: don’t trust parameters.

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 500×500 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.