Inherited rate model of the cell cycle: Kinetics of related cells, EPI-genetics of ribosomal DNA transcription and the evaluation of cancer-therapy fractionation schedules and doses

Abstract

A two-variable, stochastic model of the mammalian cell cycle is proposed for the interpretation of correlations between the intermitotic times of related cells, for the analysis of heterogeneous silver staining patterns that are seen at the nucleolar organizer regions (NORs) of chromosome spreads, for the analysis of fraction-labeled-mitoses curves and for simulating the outcome of chemotherapeutic protocols having different doses and fractionation schedules. One of the model's variables represents the chromatin condensation/eplication cycle. The second variable is related to the cell's ability to grow: the number of fibrillar centers in the cell's nucleoli, in excess of the minimum number found in quiescent cells. The number of these centers is assumed to increase and decrease at random, with transition rates that are functions of the growth conditions. The chromatin variable is postulated to increase at a rate proportional to the nucleolar variable (through a mechanism involving ubiquitin), so that the cell's generation time will also be random. The number of fibrillar centers in a mitotic mother cell persists in newly-formed daughter cells, providing a mechanism for positive correlation between sibling and mother-daughter cell generation times. Expressions for the following quantities are provided as a function of the model's parameters: the average, variance and higher moments of the intermitotic time, the distribution of the number of fibrillar centers, the joint distribution of sibling, mother and daughter cell intermitotic times, the Malthusian parameters of exponential population growth, numbers that describe the damped oscillation of a perturbed population and the entropy of a cell population.