Mini workshop in Oxford

Today Marcus Tindall has organised a mini symposium (for lack of a better name) for me and the guys here working on mathematical models of cancer to get to know each other. I have given a very small presentation [PDF] (<30m) that covers stuff I presented before.

From the CMB I got to know the work of:

• Philip Murray, who has created a CA model to study the role of the cell cycle in tumours and that is now trying to obtain a continuous model that displays the same behaviour.
• Alex Fletcher who studies hypoxia in tumour development at the sub-cellular scale.
• Matt Johnston who works with W. Bodmer (whose game theory models have inspired my own work) to study the dynamics of cell populations in a colon crypt in colorectal cancer. His model shows how a homeostatic population could explode by slightly altering some of the paramers.
• Natasha Li who collaborates with Gatenby to study, using Cellular Automaton and continuous models, the role of glycolysis in tumour invasion and the influence of the stromal environment. This is specially relevant to me since it is one of my two main lines of work at the moment. She mention in her talk that glycolytic cells are especially sensitive to glucose deprivation.
  
• Rebecca Carter works on multiscale models of fluid and drug transportation in tumours.
• Marcus Tindall gave a brief introduction to his multiscale model of interaction between the cell cycle and cell density.

The presentations were all quite short but I hope to hear more from these people in the coming days.

Somatic and non somatic evolution

Many ecologists study evolution of the non somatic kind. That is, evolution that happens as a consequence of mutations in the germ line of multicellular organisms during reproduction. The evolution of cancer is of the somatic kind. This means that it affects cells of the soma, the ones that are not transmitted to the offspring.

Some time ago I got this paper from Crespi and Summers (nicely enough, publicly available). I will probably talk about this paper, entitled Evolutionary biology of cancer (and presented to a readership of ecologists) some other time but I liked a table in which they compare somatic and non somatic evolution.

Phenotypic variation. In most ecosystems of multicellular organisms variation is attained through genetic recombination (sexual reproduction) and mutation. In a tumour we also have to consider also genomic instability (a hypothesis by which some individuals have a higher probability of mutation) and epigenetic alteration (the environment also affects the behaviour of cells in ways that could make tumour progression to cancer more or less likely).
Selection. In most ecosystems it means dealing better with competitors, avoiding predators, parasites and producing many fit successors. In a tumour means being good at competing for resources with other cells (tumour or otherwise), avoiding the immune system and coping with environmental signals designed to maintain homeostasis.
Drift. That is similar in both types of evolution.
Inheritance. In many cases that involves the transmission of genes from parents to offspring through sexual recombination. In tumours there is no sexual reproduction.
Result. In most ecosystems the result is adaptation across generations. In a tumour the end results is in many cases the death of the individual and thus of all the cells in the body, including the cancer cells.

I think that this is a quite interesting and useful comparison of evolution although I am not sure I agree with all the differences suggested. In my view the evolution in a tumour does not differ much from other types of evolution. For instance, epigenetic changes do play a role in other ecosystems asides from cancer. Genetic instability is not a source of variation, genetic mutations are (genetic instability just makes genetic mutations more likely). Also the fact that tumour cells reproduce asexually is not a big difference with more conventional ecosystems. At the end of the day most of the biomass of the planet is made of bacteria that reproduces asexually. What it is true is that as far as we know, the end result of cancer evolution is either the end of the cancer itself or the end of the individual that hosts the cancer and thus the end of the cancer cells. Thus the only way tumour cells have to be successful is to evolve in such a way that the life of the host is not threatened (you can call that tumour sustainable growth).

The laws of biology

The side effect of having spending so much time traveling these last months is that I have this stack of Nature and Science journals (I switched from the former to the latter a month ago to see the difference) which I am going through quite slowly.

In a Nature from the 7th of February there is an interesting essay about the clash of cultures between biologists and physicists working on biological topics written by a physicist from MIT (good to know where the bias will come from). Physicists have a long tradition of studying an (increasing) range of phenomena and producing theoretical models that characterise as many of those phenomena as possible. These are what are called the laws of physics. The question is if biology can have also models and laws that represent biological phenomena.

Although there are some (fairly generic and neat) biological laws (thing of Darwin's evolution and Mendel's genetics) most biologists seem to be more interested in fact collecting than in putting the available information in the form of theoretical models and universal laws of biology. The physicists (and mathematicians) coming to the field have not much knowledge in how the facts are collected (which it is easy to imagine as the source of many frustrations) but a deep interest in integrating those facts into models (especially when it involves using their favourite tools such as phase transitions, fractal analysis, power laws or networks). It remains to be seen if (in the view of the author) these general laws are possible at all and if (not my view but at least my question) the tools that were useful in physics will be that useful in biology (which does not mean they could at the very least, constitute a good starting point).

Telomeres, cancer and aging

One quite fascinating thing in animal biology is the question of immortality or, to be more precise, the lack of it. While most unicellular organisms can divide for as long as they have the luck to find resources and space to do so, human cells can divide only a limited amount of times (approximately around 50 times, although this does not apply to stem cells that can divide an unlimited amount of times). In principle the limitation in divisions for most human cells is due to a mechanism that has been evolved and is not an intrinsic limitation. The cancer hypothesis is that the limitation makes the appearance of cancer more unlikely. If a cell is limited to just a few divisions, if it acquires a mutation that mutation is unlikely to spread to far.

The reason for this limitation are the telomeres, situated at the end of the chromosomes, that get shorter each time the cell divides. Once these telomores reach a critical size and become to small the cell will enter a state called senescence by which they will not divide again.

This is an interesting link in which they talk about this and how in the next few decades we might know enough about the effects of limited cell replication in human life expectancy, how to increase it (maybe for ever) and how to do that avoiding nasty side effects (like increased probability of dying from cancer). The website in which this is hosted is covering all sorts of news, many of them of dubious scientific interest, but the information in the link looks sound.

On the other hand in a more reliable source (PNAS) there is a nice study on how telomere dysfunction can cause genetic instability. They work on a disease known as Werner syndrome but it is quite useful stuff for cancer research. This Werner syndrome results in people aging prematurely and researchers at the Salk institute have found how extra short telomeres can be the source of the problem.

The Darwinian perspective, the mutator phenotype and response to stress

Although today I will be writing about a paper recently published in the international journal of Epidemiology and authored by Paolo Vineis and Marianne Berwick, this is not going to be a review in the usual sense. This time I would like to write about the ideas and make no reference to the methodology.

The Vineis and Berwick emphasize the role of population dynamics on cancer progression. The usual view on cancer is that cancer cells grow at a faster rate than normal cells and that is the reason why they end up (if successful) killing the host. Growing populations can be due to this but they can also be the result of other factors (think of longer lifespan). The authors hint that the success of most cancers (with respect to taking over a tissue) lays on the fact that cancer cells have a greater proportion of replicating daughter cells. That makes sense to me. For instance, in a tumour whose cells that are capable of dividing near the tumour growth front (let's call them motile tumour cells) will have an advantage over other non motile but faster proliferating tumour cells in terms of how many of its daughter cells will be in position to proliferative (regardless to the speed at which they can divide).

The authors have also something to say about the highly controversial topic of the mutator phenotype. Quick reminder: the amount of time to pick up all the mutations necessary for a neoplastic cell to become a cancer cell is, according to some researchers, big enough as to be unlikely to happen in our life time. Thus cancer is the consequence of a single mutation that makes the cell more likely to produced mutated offspring. To prove their point they compare tumour cells to the behaviour of E.coli under stress. Under normal circumstances the mutation rate of the E.coli is low but when the going gets tough the mutation rates increases significantly. The speculation is that this is no accident but a feature of the bacterial DNA that in such a way can explore a genetic solution out of the problem. Could tumour cells be attempting something similar?

I find this hypothesis quite interesting and from my limited experience it seems quite novel. It should be interesting to do some experimental work (maybe more than theoretical) to see if there are any molecular mechanisms that might have an effect on the probability of mutation (say, the DNA repair mechanism) that could be held down when there are 'stress' signals in the environment. It could even be that the mechanism is similar to that of the E.coli although since bacteria are far simpler cells than human cells that could be unlikely (not having any experience with molecular biology should make any one be skeptic about statements like this).

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.

Recap from Lyon (I)

As I mentioned in a previous post one of the nice talks in Lyon came from Vito Quaranta, from Vanderbilt University in Nashville, USA.

He is and MD collaborating with researchers in the States and Europe (eg Sandy Anderson from Dundee) to develop models on tumour invasion. That is the defining feature that separates tumours from benign to malign (eg cancer).

In order to know if a cancer is invasive MDs tend to look at the way the tumour grows. A tumour with a smooth margin is unlikely to be invasive whereas one with fingering is likely to be so.

Of course I am interested to know if there are alternative studies that could be used to predict the evolution of the cancer that are not based on how the tumour shape looks like. First because in many cases physicians don't have accurate images of the contour of tumours (or sometimes haven't got enough information about what is the result of tumour growth). Second, and maybe most important, because the current shape of a tumour doesn't say much about the potential evolution of it towards malignancy. Maybe a different measure (based on the phenotypic composition of tumour cells) could help not only to tell if a tumour is malignant or benign but if the chances of becoming invasive are high or not.

In any case his presentation showed some interesting results on how the microenvironment affects the evolution of the cancer. Homogeneous microenvironments, that is, those in which space can be created with the same ease everywhere, lead to smooth contours whereas inhomogeneous ones lead to fingering. Interestingly these inhomogeneous microenvironments tend to lead to tumours with little diversity in terms of phenotype: when it is difficult for a tumour cell to create space only invasive phenotypes tend to survive.