Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Chemical Engineering

First Advisor

Martin A. Hjortso


Hairy roots produce secondary metabolites which have been used as specialty chemicals. The mathematical models of hairy root growth kinetics can guide the design and scale-up of root cultures. An unstructured segregated and a chemically structured segregated models for hairy growth kinetics are formulated with rules of root branching processes. The deterministic branching rule and the stochastic branching rule are studied. For the deterministic rule where two branching parameters are assumed constant, the number of tips can be obtained by solving a linear difference equation. The conceptual framework established for the deterministic rule is used to formulate a stochastic rule in which two branching parameters change randomly. An age population balance equation is used for the unstructured segregated model in an unchanging environment. In this model, age is assumed sufficient to describe the states of cells. Using this model, the growth kinetics of transformed roots of Tagetes erecta is studied in shake flasks in an unchanging environment. For a transient state, maturity is used as a state parameter because the rate of change in the maturity depends on its environment. For this case, a maturity population balance equation is used. The solutions of the age population balance equation and the maturity population balance equation depend explicitly on the number of tips as a function of time. It is shown how this number can be found from a set of branching rules which can either be deployed in simulation algorithms or can be used to obtain a difference equation governing the development of the tip number. Finally, a structured segregated model in the transient state is also formulated. The central assumption used in this model is that the hairy root is divided into two phases, the tip phase and the root body phase. Furthermore, the root body is assumed to consist of two compartments, cytoplasm and vacuole. The medium phase and the tip phase are modeled by the structured distributed model and the root body phase is modeled by the structured segregated model which is based on a maturity.