Abstract
Biological networks can be very complex. Mathematical modeling and simulation of regulatory networks can assist in resolving unanswered questions about these complex systems, which are often impossible to explore experimentally. The network regulating the Drosophila circadian clock is particularly amenable to such modeling given its complexity and what we call the clockwork orange (CWO) anomaly. CWO is a protein whose function in the network as an indirect activator of genes per, tim, vri, and pdp1 is counterintuitive--in isolated experiments, CWO inhibits transcription of these genes. Although many different types of modeling frameworks have recently been applied to the Drosophila circadian network, this chapter focuses on the application of continuous deterministic dynamic modeling to this network. In particular, we present three unique systems of ordinary differential equations that have been used to successfully model different aspects of the circadian network. The last model incorporates the newly identified protein CWO, and we explain how this model's unique mathematical equations can be used to explore and resolve the CWO anomaly. Finally, analysis of these equations gives rise to a new network regulatory rule, which clarifies the unusual role of CWO in this dynamical system.
