The workshop last week at Vanderbilt was very intense and unusual in the sense that, asides from the usual sessions with talks and posters there were group projects in order to get biologists and mathematicians (or other types such as computer scientists, chemists and physicists) to work together.

The group in which I worked had a fair balance of biologists and mathematicians and, apparently, a keen interest in studying the role of the protein known as TGF-Beta in prostate tumours. The project focused (and still does, since some of the people in the group will keep working on that) on producing an indivudual-cell based model that could answer questions such as :

• How does the loss of TGF-Beta responsiveness in epithelial cells (cells in the outer layer of organisms including the colon and the prostate) affect tumour initiation?
• Does the increased production of TGF-Beta affect tumour progression? and if so, how?
• What is the role of monocytes (immune cells that can be recruited by TGF-Beta and, when matured, become macrophages) in tumour progression?
• Given that TGF-Beta produces different and some times, mutually opposed effects in each cell type, is it possible to study this interplay of TGF-Beta responses in the most relevant cell types?

The results where pretty spectacular given that we had approximately a couple of days to come with the project, the model, the questions we wanted to approach with the model and some initial simulations. An example of one of these simulations can be seen in movies cell, bm, tgf and mde. Each of the movies shows a different aspect of the simulations. The cell movie shows tumour progression in a domain containing a double layer of basal and lumen cells, separated from the rest by a membrane. In the outside, as shown in the figure there are stromal cells, receptive to TGF-Beta, and monocytes, that move towards the source of TGF-Beta once the concentration reaches a certain level. After a few seconds, a mutation transforms one of the epithelial tumour cells into a tumour cell that does not consume TGF-Beta and that produces enzymes that can degrade the basal membrane which confines the cells. This alterations increase the proliferation capabilities of the tumour cell and alter the homeostatic balance. Movie bm shows how the basal membrane is degraded and vanishes. The tgf movie shows the production of TGF-beta. Magenta and red represent high concentrations. Finally the mde movie shows how the membrane degrading enzymes are produced, initially at the same rate than the membrane is rebuilt.