Modeling the Cell Cycle Using Functional Modules of Delayed, Ultrasensitive and Bistable Responses

Abstract

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that directly describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill equation. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, a bistable response is not easily modeled in such an explicit way. Here, we extend the classical Hill function into a functional module that can be used to describe both ultrasensitive and bistable responses. We show how ultrasensitive, bistable and time delay modules can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can account for events such as DNA damage and coupling to the circadian clock in a phenomenological way.