On analytical and numerical approaches to division and label structured population models

Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.