The cell cycle of budding yeast is controlled by a complex chemically reacting network of a large group of species, including mRNAs and proteins. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard for people with less training to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a website where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation. With the help of this visualization tool, we can easily and intuitively see many key steps in the budding yeast cell cycle procedure, such as bud emergence, DNA synthesis, mitosis, cell division, and the current populations of species. / Master of Science / The cell cycle of budding yeast is controlled by a complex chemically reacting network. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a webpage where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation.

<p>By using AR/ARX-models on data generated by a nonlinear differential equation system representing a model for the cell-cycle control system in budding yeast, the interactions among proteins and thereby also to some extent the genes, are sought. A method consisting of graphical analysis of differences between estimates from two local linear models seems to make it possible to separate a set of linear equations from the nonlinear system. By comparing the properties of the estimations in the linear equations a set of approximate equations corresponding well to the real ones are found. </p><p>A NARX model is tested on the same system to see whether it is possible to find the dependencies in one of the nonlinear differential equations. This approach did, for the choice of model, not work.</p>

By using AR/ARX-models on data generated by a nonlinear differential equation system representing a model for the cell-cycle control system in budding yeast, the interactions among proteins and thereby also to some extent the genes, are sought. A method consisting of graphical analysis of differences between estimates from two local linear models seems to make it possible to separate a set of linear equations from the nonlinear system. By comparing the properties of the estimations in the linear equations a set of approximate equations corresponding well to the real ones are found. A NARX model is tested on the same system to see whether it is possible to find the dependencies in one of the nonlinear differential equations. This approach did, for the choice of model, not work.

Mathematical modeling has become increasingly popular as a tool to study regulatory interactions within gene-protein networks. From the modeler's perspective, two challenges arise in the process of building a mathematical model. First, the same regulatory network can be translated into different types of models at different levels of detail, and the modeler must choose an appropriate level to describe the network. Second, realistic regulatory networks are complicated due to the large number of biochemical species and interactions that govern any physiological process. Constructing and validating a realistic mathematical model of such a network can be a difficult and lengthy task. To confront the first challenge, we develop a new modeling approach that classifies components in the networks into three classes of variables, which are described by different rate laws. These three classes serve as "building blocks" that can be connected to build a complex regulatory network. We show that our approach combines the best features of different types of models, and we demonstrate its utility by applying it to the budding yeast cell cycle. To confront the second challenge, modelers have developed rule-based modeling as a framework to build complex mathematical models. In this approach, the modeler describes a set of rules that instructs the computer to automatically generate all possible chemical reactions in the network. Building a mathematical model using rule-based modeling is not only less time-consuming and error-prone, but also allows modelers to account comprehensively for many different mechanistic details of a molecular regulatory system. We demonstrate the potential of rule-based modeling by applying it to the generation of circadian rhythms in cyanobacteria. / Ph. D.