A mathematical study on the evolution of cancer cells

Cancer is a big issue in the present age. In Japan, over 300,000 people die of cancer per year and the number is increasing. Steady achievements by molecular biology, pharmacology, genetics, immunology, bioinformatics and many other fields have revealed basic mechanisms of cancer and provide us with various effective drugs that target specific molecules of cancer cells. A lot of experimental evidence also offers us a chance to investigate the theory of cancer initiation and progression. In this talk, we present a set of theories concerning the onset of cancer by rare mutations. Sporadic retinoblastoma serves as an example of a situation in which two mutations are accumulated during clonal expansion of a cell population. We calculate the probability that the population has evolved both mutations before it reaches a certain size. Moreover we design a stochastic mathematical model of hematopoietic stem and progenitor cells to study the evolutionary dynamics of cancer initiation. We consider different evolutionary pathways leading to cancer-initiating cells in JAK2V617F-positive myeloproliferative neoplasms (MPN) and find mathematical evidence that a progenitor is the most likely cell of origin of JAK2V617F-mutant MPN. I believe that the findings on the evolution of cancer cells by the mathematical investigations contribute to the fight against the cancer.