Synchrony in a population of hysteresis-based genetic oscillators

Oscillatory behavior has been found in different specialized genetic networks. Previous work has demonstrated nonsynchronous, erratic single-cell oscillations in a genetic network composed of nonspecialized regulatory components and based entirely on negative feedback. Here, we present the construction of a more robust, hysteresis-based genetic relaxation oscillator and provide a theoretical analysis of the conditions necessary for single-cell and population synchronized oscillations. The oscillator is constructed by coupling two subsystems that have previously been implemented experimentally. The first subsystem is the toggle switch, which consists of two mutually repressive genes and can display robust switching between bistable expression states and hysteresis. The second subsystem is an intercell communication system involved in quorum-sensing. This subsystem drives the toggle switch through a hysteresis loop in single cells and acts as a coupling between individual cellular oscillators in a cell population. We demonstrate the possibility of both population synchronization and suppression of oscillations ( cluster formation), depending on diffusion strength and other parameters of the system. We also propose the optimal choice of the parameters and small variations in the architecture of the gene regulatory network that substantially expand the oscillatory region and improve the likelihood of observing oscillations experimentally.