Figure 4.
Stochastic oscillations in even rings and readout-based control. (a) Illustration of the readout-based control scheme for a ring of six genes. Two proteins of the ring are read out with fluorescent tags. This readout is then compared with a reference defined according to the oscillating behaviour of the ring, with similar period and a shift between consecutive genes. The reference comparison is threshold-based and leads to an ON–OFF (1–0) control for the KICK signals. These can be implemented with light-responsive gene promoters. In the numerical simulations shown in (b), the KICK signals are indicated with the red markings in the upper panels. (b) A simple readout-based control reliably switches on the oscillations, sustains them and switches them off. The control mechanism functions by monitoring two successive proteins in the ring. Whenever each of them falls below a threshold, a KICK signal for the corresponding protein is given. These threshold-based KICK signals are indicated with red and magenta markings in the upper panels. The oscillation can be terminated with a STOP signal as in the deterministic state. The optical readout can be based on GFP or YFP protein labelling, while the response can be implemented with on-demand UV or red light that enhances the production of the corresponding mRNAs (Shimizu-Sato et al. 2002). The figure shows the application of this mechanism to a ring with n = 10. The stochastic time traces correspond to the protein expression of proteins pj with j = 1, 3, 5, 7, 9 and the corresponding control (top) in response to proteins p1 and p2 (trace not shown). The right figure is a magnification of the dashed square inside the main figure. We have also checked that this control protocol is applicable for rings with as low as n = 6 genes (not shown).