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.
Keywords: Poincaré−Bendixson theorem; epigenetic memory system; model-based design; monotone control system; negative feedback control; synthetic oscillator.