TABLE OF CONTENTS Even steady-state population balance models are so mathematically complex that analytical solutions are possible only in special cases. However, it is possible to obtain models that are mathematically quite simple by making use of the concept of cell cycle control points. Although crude, control point models can be solved analytically and the solutions do provide valuable insight into the properties of the distribution of states and how it changes with growth conditions and with different kinds of cell cycle controls. Working with these simple control point models also builds one's insight and intuition about population balances and their solutions, intuition that can be extremely valuable when progressing to analysis of more realistic models. This chapter first covers control point models in some depth before describing the special cases in which analytical solutions can be obtained without the assumption of control points.
Living cells differ from almost all other types of particles in that growth and division processes are tightly controlled by groups of regulatory proteins usually known as the cell cycle control system [2]. The details of the control system vary from organism to organism, but all must direct the replication of the genome prior to cell division and the partitioning of the two genome copies as well as other essential cell components and organelles between the two daughter cells formed in the division. The cell cycle control system is similar in all eukaryotes and is customarily divided into a sequence of consecutive phases, the G1,...
