Balance of cell proliferation and death among dynamic populations: a mathematical model.
Developmental changes in cell numbers represent the dynamic balance between cell proliferation and death. One obstacle to assessing this balance is an inability to quantify the total amount of cell death, i.e., with a positive indicator such as terminal dUTP nick end labeling (TUNEL) or caspase activity. A novel mathematical model is described wherein data on daily cell growth (the change in cell number) and cell cycle kinetics can be used to determine the total amount of cell death. Two sets of data from previously published studies were tested in this model; primary cultured cortical neurons and B104 neuroblastoma cells. These two preparations have contrasting features: neuronal cultures are heterogeneous and have relatively few cells that are actively cycling (i.e., the growth fraction for these cells is low), whereas B104 cells are relatively homogeneous cultures in which the growth fraction is high. In primary cortical cultures, there was a balance in cell production and death. Treatment with a potent anti-mitogen, ethanol (400 mg/dl), affected this balance principally by reducing cell production, although the rate of cell death was also increased. In untreated B104 cells, there was eight-fold more cell production than cell death. Growth factors such as platelet-derived growth factor BB doubled cell production. Ethanol reduced cell production by >60%, and it eliminated growth factor-mediated cell production. All of these changes occurred in the absence of an effect on the amount of cell death. Thus, the model is ideal for predicting the effects of an epigenetic factor (e.g., a growth factor, toxin, or pharmacological agent) on cell development and can be useful in determining the consequences of a genetic manipulation as well.