This project concerns the development of mathematical models of biochemical oscillations and the analysis required to understand their underlying behavior. While the list of molecular systems that exhibit oscillations is growing, the grasp of the common principles is challenged by the variety of underlying network structures. The presence of negative feedback is the only feature shared by all oscillatory networks; beyond this each system seems to be unique. The goal is to formulate a common principle that is shared by all oscillatory networks. It is expressed in terms of broad tendencies of the dynamics, rather then the detailed structure of the supporting networks. Cells constantly communicate with their environment and their neighbors. This mutual communication often results in synchronization of their behavior. A theory will be developed to explain synchronization of periodic signals in cell communities. The synchronization of biochemical oscillators will be studied via the nearest neighbor coupling, and the coupling with a communally produced and sensed molecule.
A recent unprecedented explosion in our knowledge of structure and function of genetic regulatory networks promises revolutionary changes in how human disease is viewed and treated. Many biological processes ranging from the cell cycle to the human 24 hour circadian rhythm are periodic in time. This periodicity is driven by oscillations in the concentration of chemicals in individual cells. In many cases these signals synchronize across populations and the periodic signal can be detected on a macroscopic level. The regulatory networks that are responsible for production and maintenance of these rhythms are being discovered every day. While the structures of these networks vary, they often produce similar periodic signals. This project will study the underlying broad dynamics principles behind the oscillations, emphasizing the function of the network over its implementation. Further, it will study synchronization of the periodic rhythms in population of cells. The lack of synchronization in the population can result in developmental and functional defects. This project will develop a theory that will be able to predict collective dynamics, as well as suggest repair mechanisms in the case of failure.
