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Number 3 - September 2025
Volume 35 - 2025
Modeling propagation of weakly advantageous mutations in cancer cells
Andrzej Polański, Mateusz Kania, Jarosław Gil, Wojciech Łabaj, Ewa Lach, Agnieszka Szczęsna
Abstract
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.
Keywords
cancer evolution, Gillespie algorithm, mutation wave modeling