# Dynamical Modeling in Cell Biology with Ordinary Differential Equations

## Degree

Doctor of Philosophy (PhD)

## Department

Biological Sciences

Dissertation

## Abstract

Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected by other researchers led to apparently straight-forward conclusions based on experimental techniques. However, this is contradicted once a dynamical model is applied to the system. I show that interpretation of data that comes as a snapshot of a dynamical system is a dynamical modeling problem, even if one can fit a nice linear regression to that data. In chapters 2 and 3 I demonstrate the value of added complexity to mathematical models in firefly luciferase. Usually, a simple solution is considered best, but this may leave information behind. By expressing the simplified Michaelis-Menten model as a system of differential equations we are able to get valuable parameter estimates. These parameter estimates would be otherwise costly. In addition, the model allows us to quantify trends in the data that are visible but not interpretable by scientists without a mathematical framework. In chapter 4, a problem without experimental data is tackled regarding the plant cell cycle and its switch to endoreplication. In this case, much tedious hand-fitting is required to answer the research questions. Using this technique I was able to address biological questions, understand the validity of the model and the biological assumptions that went into that model. In chapter 5 I motivated the further development of educational tools to disseminate modeling and computational techniques to biologists. This type of training is necessary for the future of the field.

11-18-2019

Kato, Naohiro