Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis. Other mutations, however, do not change the phenotype of the cell or even decrease cellular fitness. While much experimental effort is being devoted to the identification of the functional effects of individual mutations, mathematical modeling of tumor progression generally considers constant fitness increments as mutations are accumulated. In this paper we study a mathematical model of tumor progression with random fitness increments. We analyze a multi-type branching process in which cells accumulate mutations whose fitness effects are chosen from a distribution. We determine the effect of the fitness distribution on the growth kinetics of the tumor. This work contributes to a quantitative understanding of the accumulation of mutations leading to cancer.
Bibliographical noteFunding Information:
The first author was partially supported by NSF grant DMS 0704996 from the probability program. The second author was partially supported by NIH grant R01CA138234 . The third author was partially supported by NIH grant U54CA143798 . The fourth author was partially supported by NSF RTG grant DMS 0739164 . The fifth author was partially supported by NIH grants R01CA138234 and U54CA143798 , a Leon Levy Foundation Young Investigator Award, and a Gerstner Young Investigator Award.
- Beneficial fitness effects
- Branching process
- Cancer evolution
- Fitness distribution
- Mutational landscape