A comprehensive continuous-time model for the appearance of CGH signal due to chromosomal missegregations during mitosis

Aneuploidy, the gain or loss of large regions of the genome, is a common feature in cancer cells. Irregularities in chromosomal copy number caused by missegregations of chromosomes during mitosis can be visualized by cytogenetic techniques including fluorescence in situ hybridization (FISH), spectral karyotyping (SKY) and comparative genomic hybridization (CGH). In the current work, we consider the propagation of irregular copy numbers throughout a cell population as the individual cells progress through ordinary mitotic cell cycles. We use an algebraic model to track the different copy numbers as states in a stochastic process, based on the model of chromosome instability of Gusev, Kagansky, and Dooley, and consider the average copy number of a particular chromosome within a cell population as a function of the cell division rate. We review a number of mathematical models for determining the length of the cell cycle, including the Smith-Martin transition probability model and the 'sloppy size' model of Wheals, Tyson and Diekmann. The program MITOSIM simulates the growth of a population of cells using the aforementioned models of the cell cycle. MITOSIM allows the cell population to grow, with occasional resampling, until the average copy number of a given chromosome in the population reaches a preset threshold signifying a positive copy number alteration in this region. MITOSIM calculates the relationship between the missegregation rate and the growth rate of the cell population. This allows the user to test hypotheses regarding the effect chromosomal aberrations have upon the cell cycle, cell growth rates, and time to population dominance.