Cell cycle kinetics with supramitotic control, two cell cycles, and unequal division: A model of transformed embryonic cells

We develop a mathematical model of cell cycle kinetics of transformed embryonic cells. The model includes supramitotic regulation, in which decisions regarding growth control are made at a point inside the cell division cycle and their impact extends to the next decision point, located in the next division cycle. Another feature is the presence of two varieties of cells, which switch from one to the other with given transition probabili-ties. The third factor considered is unequal division of cells, also defined in probabilistic terms. We provide a rigorous description of the model and derivation of its equations and analyze its asymptotic properties by defining and investigating an abstract semigroup of positive linear operators in appropriate state space. The spectral properties of the semigroup yield the balanced exponential growth law for the model. To compare the model to experimental data, we derive basic pedigree statistics, p curves, and generation time correlations. We present numerical calculations based on measurements available for the embryonic cells. We conclude that to yield the experimen-tally obtained pedigree statistics, switches from one cell variety to the other must be quite infrequent. 1