Oscillations are an important component in biological systems; grasping their mechanisms and regulation, however, is difficult. Here, we use the theory of dynamical systems to support the design of oscillatory systems based on epigenetic control elements. Specifically, we use results that extend the Poincaré–Bendixson theorem for monotone control systems that are coupled to a negative feedback circuit. The methodology is applied to a synthetic epigenetic memory system based on DNA methylation that serves as a monotone control system, which is coupled to a negative feedback. This system is generally able to show sustained oscillations according to its structure; however, a first experimental implementation showed that fine-tuning of several parameters is required. We provide design support by exploring the experimental design space using systems-theoretic analysis of a computational model.

In previous work, we have developed a DNA methylation-based epigenetic memory system that operates in Escherichia coli to detect environmental signals, trigger a phenotypic switch of the cells and store the information in DNA methylation. The system is based on the CcrM DNA methyltransferase and a synthetic zinc finger (ZnF4), which binds DNA in a CcrM methylation-dependent manner and functions as a repressor for a ccrM gene expressed together with an egfp reporter gene. Here, we developed a reversible reset for this memory system by adding an increased concentration of ZnSO 4 to the bacterial cultivation medium and demonstrate that one bacterial culture could be reversibly switched ON and OFF in several cycles. We show that a previously developed differential equation model of the memory system can also describe the new data. Then, we studied the long-term stability of the ON-state of the system over approximately 100 cell divisions showing a gradual loss of ON-state signal starting after 4 days of cultivation that is caused by individual cells switching from an ON-into the OFF-state. Over time, the methylation of the ZnF4-binding sites is not fully maintained leading to an increased OFF switching probability of cells, because stronger binding of ZnF4 to partially demethylated operator sites leads to further reductions in the cellular concentrations of CcrM. These data will support future design to further stabilize the ONstate and enforce the binary switching behaviour of the system. Together with the development of a reversible OFF switch, our new findings strongly increase the capabilities of bacterial epigenetic biosensors. AbbreviationsCcrM, Caulobacter crescentus cell-cycle-regulated methyltransferase; ZnF, synthetic zinc finger protein; ZnF4, homotetramer of the ZnF protein.