Hybrid Modeling and Simulation of Biomolecular Networks

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feed-back pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes a hybrid systems approach to modeling the intra-cellular network using continuous differential equations to model the feedback mechanisms and mode-switching to describe the changes in the underlying dynamics. We use two case studies to illustrate a modular approach to modeling such networks and describe the architectural and behavioral hierarchy in the underlying models. We describe these models using CHARON [2], a language that allows formal description of hybrid systems. We provide preliminary simulation results that demonstrate how our approach can help biologists in their analysis of noisy genetic circuits. Finally we describe our agenda for future work that includes the development of models and simulation for stochastic hybrid systems.