*Speaker: Louis Vermeulen*

*Department: JNI Oncology*

*Subject: Stem cell dynamics in homeostasis and cancer of the gut*

*Location: Erasmus MC*

*Date: 23-3-16*

* Author: Hielke Walinga
*

A good way to look to cancer in the biological sense is to see it as a process of evolution on the cellular level. A cancer cell is fitter than the healthy cells because it produces more offspring, and is not killed by apoptosis. In this way cancer can better be understood by studying the dynamics between cells and so discover what is responsible for a larger offspring in the cells. The cells that produce offspring in an organism are exclusively the stem cells. Studying stem cell dynamics is therefore very important in a better understanding of cancer. This is what Louis Vermeulen discussed in his seminar on 23 March. Louis Vermeulen has studied the stem cell dynamics of the intestinal stem cells (ISC’s) and proposed a model describing these dynamics and how certain cancer mutations alter these dynamics.

First of all research has shown that colon cancer isn’t a bulk of cells growing very fast, but it looked like these cancer create a bit their own small organized organs. This is, however, simply explained by the fact that these cancers didn’t arise from random cells, but did arise from stem cells. Therefore they grow still in a bit organized manner.

The inside of the intestine consists of a lot of relief, because it is covered with so-called villi. The cells in these villi got lost pretty fast and of course need to be replaced. The stem cells replacing these are located at the bottom between these villi. Replacing is therefore from the bottom to the top. In this well the ISC’s are located in a circle. Not only did these ISC’s replace the cells above them, but it turned out they also replace each other. This is discovered by the use lineage tracing. The stem cells are marked by something which is also visible in their offspring.

After this discovery they tried to model this stochastic dance of replacing. They discovered that their model was sufficient by taking only two parameters, N and λ. N is the number of ISC who participate in the dance and λ is the replacement rate of ISC’s per time unit. It turned out that the dance is so dynamic that there is a good chance that one ISC will replace all the others. This is called fixation, and obviously the fixation chance is the important value which a cancer cell is trying to increase.

When all ISC’s are healthy (i.e. no cancer cells) the chance that one ISC will replace its neighbor is just 50 percent. A cancer cell will of course have a higher chance to do this. When this chance is known the fixation chance can be calculated by the following formula.

*Image 1: Formula for chance of fixation, P _{fix}, with the amount of ISC, N, and the increased chance of replacing its neighbor, P_{R} (for neutral drift this is 0.5).*

Later research has shown that certain cancer mutations indeed have a bias in this drift. These mutations are: KRAS^{G120}, APC^{+/-}, APC^{-/-}. Important to know is the a very frequent cancer mutation, p53^{R172N}, is not creating a bias.

I think this research perfectly shows how mathematical models can give more insight in something biological complex as oncogenesis.

*Image 2: This image shows how a fixation event takes place.*