Modeling Propagation of Weakly Advantageous Mutations in Cancer Cells

There is recent evidence that a considerable proportion of somatic mutations in cancer cells’ DNA may exert a weakly advantageous effect on tumor growth. In this paper, we develop models of cancer evolution with somatic mutations that introduce a weakly advantageous force to the evolution of cancer cells. The elaborated models incorporate random events of cellular births, deaths and occurrences of somatic mutations in cancer cells’ DNA. The models belong to two categories: deterministic and stochastic. The former are based on systems of differential equations that balance the average number of cells and mutations during evolution. To verify the results of our deterministic modeling, we use a stochastic Gillespie algorithm. We show that our models predict the explosive growth of the cancer cells population, consistent with recent experimental observations.