In this article, we study the coupling of a collection of molecular oscillators, called repressilators, interacting indirectly through enzymatic saturation. We extended a measure of autocorrelation to identify the period of the whole system and to detect coupling behaviors. We explored the parameter space of concentrations of molecular species in each oscillator versus enzymatic saturation, and observed regions of uncoupled, partially, or fully coupled systems. In particular, we found a region that provided a sharp transition between no coupling, two coupled oscillators, and full coupling. In practical applications, signals from the environment can directly affect parameters such as local enzymatic saturation, and thus switch the system from a coupled to an uncoupled regime and vice-versa. Our parameter exploration can be used to guide the design of complex molecular systems, such as active materials or molecular robot controllers.
Keywords: enzymatic coupling; molecular robotics; repressilator; synchronization.