State-vector models of the cell cycle 1. Parametrization and fits to labeled mitoses data

In this paper we study the Hahn model of the cell cycle from the point of view that a cell population's age distribution is more relevant to labeled mitoses data than is the distribution of its transit times.Closed-form relationships are derived between the transition probabilities of the Hahn model and the transit time of the mean of a cohort of labeled cells (with the variance of their transit time through mitosis). Constraints result which define the acceptable values for the number of ages in the state vector and the length of the time step (rarely does the dimension of the state vector equal the number of time steps in the generation time).A generalization to distinct probabilities for G₁, S and G₂M is presented, and the automatic fitting of fraction-labeled mitoses (FLM) data is described. The doubling time of the population is used to define the daughter factor, via the largest eigenvalue of the state transition matrix. The performance of the generalized Hahn model is compared to that of other commonly used fitting methods using two sets of FLM data from the literature. The synthesis of continuous labeling curves is discussed as an independent check of the parametrization. Based on the stable age distribution resulting from fits to experimental FLM data, it is shown that a nonlinear relationship exists between biological age and time.