Stochastic modelling of chromosomal segregation: errors can introduce correction.

Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.

Genetic Diversity in Normal Cell Populations is the Earliest Stage of Oncogenesis Leading to Intra-Tumor Heterogeneity.

Random mutations and epigenetic alterations provide a rich substrate for microevolutionary phenomena to occur in proliferating epithelial tissues. Genetic diversity resulting from random mutations in normal cells is critically important for understanding the genetic basis of oncogenesis. However, evaluation of the cell-specific role of individual (epi-)genetic alterations in living tissues is extremely difficult from a direct experimental perspective. For this purpose, we have developed a single cell model to describe the fate of every cell in the uterine epithelium and to simulate occurrence of the first cancer cell. Computational simulations have shown that a baseline mutation rate of two mutations per cell division is sufficient to explain sporadic endometrial cancer as a rare evolutionary consequence with an incidence similar to that reported in SEER data. Simulation of the entire oncogenic process has allowed us to analyze the features of the tumor-initiating cells and their clonal expansion. Analysis of the malignant features of individual cancer cells, such as de-differentiation status, proliferation potential, and immortalization status, permits a mathematical characterization of malignancy at the single cell level and a comparison of intra-tumor heterogeneity between individual tumors. We found, under the conditions specified, that cancer stem cells account for approximately 7% of the total cancer cell population. Therefore, our mathematical modeling describes the genetic diversity and evolution in a normal cell population at the early stages of oncogenesis and characterizes intra-tumor heterogeneity. This model has explored the role of accumulation of a large number of genetic alterations in oncogenesis as an alternative to traditional biological approaches emphasizing the driving role of a small number of genetic mutations. A quantitative description of the contribution of a large set of genetic alterations will allow the investigation of the impact of environmental factors on the growth advantage of and selection pressure on individual cancer cells for tumor progression.