A stochastic model of chromosome segregation errors with reference to cancer cells

A majority of tumor cells have an abnormal number of chromosomes, and this number varies even among the cells of clonal origin. Recent publications suggest that the acquisition of chromosome numerical abnormalities is an early event in a carcinogenesis pathway. Chromosomal instability may also play an important role in tumor progression. However, the mechanisms that result in abnormal number of chromosomes are poorly understood. One of the possible sources of chromosomal instability is a failure of chromosomes to segregate to the proper cells during cell division. We now propose a stochastic model that describes the evolution of chromosome number in a population of dividing cells as a result of such chromosome segregation errors (CSE). Assuming the independence of life cycles for all chromosomes within a cell, our model describes a process of evolution of cell karyotypes as a random branching walk in a K-dimensional nonnegative integer space (K = 23 for human cells). The conditions of cell death define K absorption boundaries for this random walk. Our basic model of human cells has all absorption boundaries set to zero. In the model, we have introduced a single parameter, a probability of segregation errors, which reflects an average rate of segregation errors per cell division. Using this model, we have examined the possible impact of CSE on chromosome numerical changes in cell populations. The model was implemented in a C++ program based on a discrete event simulation algorithm. Using computer simulation experiments, we have tested the sensitivity of our model to the initial conditions and parameter values. We have examined the effects of CSE on survival of cells and clones as well as on the dynamics of population growth and chromosome number distributions. Our modeling results suggest that the long-term dynamics of cell population growth depends upon the rate of segregation errors. The fraction of clones surviving was estimated as a function of the probability of CSE, and critical values for the probability of CSE were approximated which separates qualitatively different patterns of model behavior. The model suggests a theoretical limit for the rate of CSE that would allow a diploid population to survive without a complete loss of any chromosome type. It also suggests a minimal interval of probability of CSE values for which 100% survival of clones is possible. Our modeling results allow comparisons to be