Last Wednesday I was fortunate enough to be in a workshop at the University of Toronto’s Fields Institute when Nowak came to deliver a series of lectures, the first of which was on the evolutionary dynamics of cancer.
Martin Nowak is an Austrian biomathematician working at Harvard on evolution at the theoretical level. He has recently published a book on evolutionary dynamics (evolutionary dynamics understood as the mathematical study of evolution, not just in cancer).
Nowak uses the techniques described in that book to study two cancer related problems:
1- Is genetic instability a driving force of cancer progression? That is, is it an early event necessary for tumour progression?
Cancers are aneuploid which can be the result of either Chromosomal (known as CIN, an increase rate of chromosomes losing or gaining arms during cell division) or Microsatellite instability (known as MIN, an increase in point mutations in the order of up to 3 orders of magnitude). 15% of colon cancers (and a smaller proportion of other solid cancers) have MIN. In his model Nowak showed how some genetic mutations can get fixated in a population even when previous mutations required for that mutation to be competitive, don’t reach fixation through a process called tunnelling.
2- What are the dynamics of chonic myeloid leukemia.
Conventional chemotherapy is dangerous as it kills healthy cells as well as tumour cells. The reason chemotherapy does not always kill a tumour is because it has to be administered in a way that it will not do so by also killing the patient. That is the reason why targeted therapy holds such a good promise: because it kills only cells that display certain properties present only among the tumour cell population. One such drug Nowak is studying (modelling theoretically) is Imatinib which targets cells with a chromosome called Philadelphia (arising by a translocation between chromosomes 9 and 22). The translocation affects both the stem cell in which, in all likelihood, it first appears, and the progenitor and differentiated cells which are the best targets Imatinib. Some questions that can be studied mathematically (with ordinary differential equations in the case of Nowak) are the effect of point mutations that could confer resistance to the drug or why Imatinib kills differentiated cells but not stem cells. Interestingly the model predicts that despite the success of the drug there is no decline in the cancer cell population that drives the disease.
