The impact of maturation time distribution on the stage structure of a cellular population

Abstract

Here we study how the stage structure of a population of cells varies with the distributions of times spent in each stage (which we will refer to as maturation time distributions). We consider a model with two life stages. The first stage represents the beginning of the first gap phase (early G1 phase). The second stage includes the end of the G1 phase, the synthesis phase (S phase), the second gap phase (G2 phase), and the mitosis phase (M phase). The evolution of the age density of cells in each stage is governed by a system of partial differential equations (PDEs) which is presented in Chapter 1. We use the method of characteristics to prove existence of solutions to the model PDE system in Chapter 2. In Chapter 3 we discuss the computation of the maturation rate and the numerical simulation of the system of PDEs. In Chapter 4 we simulate the model using two alternative maturation time distributions in order to illustrate the importance of the maturation time distribution for the population's stage and age structure. Because drug therapies may target specific cell cycle stages, this work can inform future studies aimed at developing more efficient drug therapies.