Stochastic Mathematical Models of Carcinogenesis

Abstract

Geneticists and molecular biologists have demonstrated that car- cinogenesis is a stochastic multi-stage process with each cancer tumor being derived from a single stem cell which has sustained a finite number of genetic and/or epigenetic changes (Tan 1991, Wienberg 2007, Tan, Chen and Zhang, 2008). These genetic and/ or epigenetic changes initiate and facilitate cancer progression by driving and disturbing some relevant molecular signal pathways to promote cell proliferation and growth of cancer stem cells. In order for the biological findings to be tested quantitatively against human epidemiological data and animal experimen- tal data, and in order to develop efficient controlling strate - gies for human cancer, it is absolutely essential that these biological findings be transformed into stochastic math- ematical models. This calls for the development of biologi- cally based stochastic mathematical models for human cancers. To serve as an example, consider the human colon cancer which has been shown to be developed mainly by two multi-stage path- ways- the APC--Catenin-Tcf-myc pathway (denoted by N -> I1 -> I2 -> I3 -> I4 -> Tumor, a 4-stage stochastic pathway) and the Micro- Satellite Instability pathway (denoted by N -> J1 -> J2 -> J3 -> J4 -> J5 -> Tumor, a 5-stage stochastic pathway) (Tan et al. 2008). Biologists have shown that the I2 cells and the J3 cells divide stochastically to generate polyps which form the basis for the colon screening procedure colonoscopy. To evaluate the efficiency and usefulness of this cancer screening rocedure it is absolutely necessary to develop stochastic mod- els for human colon cancer. To serve as another example, con- sider the pediatric human eye cancer-retinoblastoma which is initiated by the mutation or deletion or inactivation of the ret- inoblastoma gene (the Rb gene) in chromosome 13q. As many other pediatric human cancers (e.g. Wilms's tumor, hepatoblas- toma, medulloblastoma, etc.), for retinoblastoma a large num- ber of cancer cases develop at and before birth during pregnant period. This calls for the development of stochastic models in- volving population genetics to involve inherited cancer cases. Based on the above and many other molecular and genetic findings (Weinberg, 2007), this short note calls for the development of sto- chastic mathematical models for human pediatric and adult can- cers. To conclude, we quote Weinberg (2007, Page 794. The Biol- ogy of Cancer. Garland Sciences, Taylor and Frances, New York): Image a day-still years away-when the biological responses of various human cells, normal and malignant, can be predicted by mathematical models of these cells and their internal circuits. Such advances will render many current practices in experimental biolo- gy, including many steps of drug development, unnecessary. If this even becomes possible, drug development will be more a matter of dry bioinformatics than wet biology at the laboratory bench.