Mathematical modeling approaches for dynamical analysis of protein regulatory networks with applications to the budding yeast cell cycle and the circadian rhythm in cyanobacteria

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Tech


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.



Cyanobacteria, Mathematical Modeling, Protein Regulatory Networks, Budding Yeast Cell Cycle, Circadian Rhythm