Synchronizing genetic oscillators by signaling molecules.

The authors examine collective rhythms in a general multicell system with both linearly diffusive and nondiffusive couplings. The effect of coupling on synchronization through intercellular signaling in a population of Escherichia coli cells is studied. In particular, a synchronization solution is given through the auxiliary individual system for 2 types of couplings. The sufficient conditions for the global synchronization of such a coupled system are derived based on the Lyapunov function method. The authors show that an appropriate design of the coupling and the inner-linking matrix can ensure global synchronization of the coupled synthetic biological system. Moreover, they demonstrate that the dynamics of an individual cell with coupling and without coupling may be qualitatively different; one is oscillatory, and the other is steady state. The change from a nonoscillatory state to an oscillatory one is induced by appropriate coupling, which also entrains all cells to synchronization. These results establish not only a theoretical foundation but also a quantitative basis for understanding the essential cooperative dynamics, such as collective rhythms or synchronization, in a population of cells.