The cyanobacterial circadian clock couples to pulsatile processes using pulse amplitude modulation

Cellular processes are dynamic and often oscillatory, requiring precise coordination for optimal cell function.^{1,2,3,4,5,6,7} How distinct oscillatory processes can couple within a single cell remains an open question. Here, we use the cyanobacterial circadian clock^8,9 as a model system to explore the coupling of oscillatory and pulsatile gene circuits. The cyanobacterial circadian clock generates 24-h oscillations in downstream targets^{10,11,12,13,14,15} to time processes across the day/night cycle.^{9,16,17,18,19,20,21,22} This timing is partly mediated by the clock's modulation of the activity of alternative sigma factors,^14,23,24,25 which direct RNA polymerase to specific promoters.²⁶ Using single-cell time-lapse microscopy and modeling, we find that the clock modulates the amplitude of expression pulses of the alternative sigma factor RpoD4, which occurs only at cell division. This pulse amplitude modulation (PAM), analogous to AM regulation in radio transmission,²⁷ allows the clock to robustly generate a 24-h rhythm in rpoD4 expression despite rpoD4's pulsing frequency being non-circadian. By modulating cell division rates, we find that, as predicted by our model, PAM regulation generates the same 24-h period in rpoD4 pulse amplitude over a range of rpoD4 pulse frequencies. Furthermore, we identify a functional significance of rpoD4 expression levels: deletion of rpoD4 results in smaller cell sizes, whereas an increase in rpoD4 expression leads to larger cell sizes in a dose-dependent manner. Thus, our work reveals a link between the cell cycle, clock, and RpoD4 in cyanobacteria and suggests that PAM regulation can be a general mechanism for biological clocks to robustly modulate pulsatile downstream processes.