Transition Probability Cell Cycle Model Part I—Balanced Growth

A cell cycle model based on the concept of a transition probability first proposed by Smith & Martin has been implemented as a differential equation model. The probabilistic A-state is modeled as a lumped parameter while the deterministic B-phase is modeled as a distributed parameter, and analytical solutions for both the population and the fraction of labelled mitosis (FLM) curves are derived under balanced growth conditions. Contributions toward cell cycle variability by single and double random transitions are considered. A double transition model provides a more realistic description of the cell cycle time distribution. For gross cell population behavior, a single transition from the A-state to the B-phase may provide acceptable approximation. In spite of the simplification, the single transition Smith & Martin model is shown to describe the gradual asynchronization of a cell population.