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 su ggest that the acquisition of chromosome numerical abnormalities is an earl y 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 possib le sources of chromosomal instability is a failure of chromosomes to segreg ate to the proper cells during cell division. We now propose a stochastic m odel that describes the evolution of chromosome number in a population of d ividing cells as a result of such chromosome segregation errors (CSE). Assu ming the independence of life cycles for all chromosomes within a cell, our model describes a process of evolution of cell karyotypes as a random bran ching walk in a K-dimensional nonnegative integer space (K = 23 for human c ells). 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 probabi lity of segregation errors, which reflects an average rate of segregation e rrors per cell division. Using this model, we have examined the possible im pact of CSE on chromosome numerical changes in cell populations. The model was implemented in a C++ program based on a discrete event simulation algor ithm. Using computer simulation experiments, we have tested the sensitivity of our model to the initial conditions and parameter values. We have exami ned the effects of CSE on survival of cells and clones as well as on the dy namics of population growth and chromosome number distributions. Our modeli ng results suggest that the long-term dynamics of cell population growth de pends 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 lim it for the rate of CSE that would allow a diploid population to survive wit hout a complete loss of any chromosome type. It also suggests a minimal int erval of probability of CSE values for which 100% survival of clones is pos sible. Our modeling results allow comparisons to be made with observations on tumors that have originated from a single progenitor cell and with the r esults of in vitro experiments on single cell derived clones. (C) 2000 Else vier Science Ltd. All rights reserved.