From cellular properties to population asymptotics in the Population Balance Equation

TL;DR

This paper uses asymptotic analysis of the Population Balance Equation to explain the exponential tails in protein distributions of proliferating cell populations, highlighting the roles of protein production and cell division.

Contribution

It demonstrates that the exponential tail in protein distributions is primarily determined by cell division and protein production, independent of other factors, providing a universal explanation.

Findings

Exponential tails are driven by cell division and protein production.

Tail behavior is insensitive to other model details.

Results align with experimental observations.

Abstract

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.