Modeling and Analyzing Biological Oscillations in Molecular Networks Techniques based on dynamical and control theories, for representing the synchronization of signals between cells, can be used to reduce the complexity of modeling biological systems.

One of the major challenges for postgenomic biology is to understand how genes, proteins, and small mole- cules dynamically interact to form molecular networks which facilitate sophisticated biological functions. In this paper, we present a survey on recent developments on modelling mole- cular networks and analyzing synchronization of bio-oscillators in multicellular systems from the viewpoint of systems biology. Attention will be focused on deriving general theoretical results to understand the dynamical behaviors of biological systems based on nonlinear dynamical and control theory. Specifically, we first describe the stochastic and deterministic approaches to model molecular networks and give a brief comparison between them. Then, we explain how to construct a molecular network, in particular, a gene regulatory network with specific functions, e.g., switches and oscillators, in individual cells at the molecular level by using feedback systems, and how to model a general multicellular system with the consideration of external fluctuations and intercellular coupling to study the general cooperative behaviors for a population of bio-oscillators. Finally, as an illustrative example, a synthetic multicellular system is designed to show how synchronization is effectively achieved and how dynamics of individual cells is efficiently controlled. Some recent developments and perspectives of analysis on biological oscillations in future are also discussed.