Steady-State Size Distributions in Probabilistic Models of the Cell Division Cycle

A model for the steady-state size distribution in an exponentially growing population of single cells is derived and studied. The model incorporates a general growth law for individual cells and a probability density for interdivision times. A uniqueness theorem is proved, and it is shown that no solution exists when individual cells grow exponentially. For linear growth, infinite series solutions are found in two specific cases. Statistical data are obtained for these solutions, and comparisons are made with the results of some numerical simulations and some experiments.