Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.