When lowering temperature, the in vivo circadian clock in cyanobacteria follows and surpasses the in vitro protein clock trough the Hopf bifurcation

TL;DR

This study investigates how the in vivo circadian clock in cyanobacteria responds to temperature changes, revealing it follows and surpasses the in vitro protein clock through a Hopf bifurcation, using a Stuart-Landau oscillator model.

Contribution

It demonstrates that the in vivo cyanobacterial clock exhibits similar bifurcation behavior to the in vitro protein clock and introduces simplified models for temperature dependence of circadian oscillations.

Findings

Both in vivo and in vitro clocks undergo a supercritical Hopf bifurcation.

The in vivo clock's response can be modeled by a Stuart-Landau oscillator.

Temperature-dependent feedback models describe the circadian response.

Abstract

The in vivo circadian clock in single cyanobacteria is studied here by time-lapse fluorescence microscopy when the temperature is lowered below 25{\deg}C . We first disentangle the circadian clock behavior from the bacterial cold shock response by identifying a sequence of "death steps" based on cellular indicators. By analyzing only "alive" tracks, we show that the dynamic response of individual oscillatory tracks to a step-down temperature signal is described by a simple Stuart-Landau oscillator model. The same dynamical analysis applied to in vitro data (KaiC phosphorylation level following a temperature step-down) allows for extracting and comparing both clock's responses to a temperature step down. It appears, therefore, that both oscillators go through a similar supercritical Hopf bifurcation. Finally, to quantitatively describe the temperature dependence of the resulting in vivo and in vitro Stuart-Landau parameters $\mu(T)$ and $\omega_c(T)$, we propose two simplified analytical models: temperature-dependent positive feedback or time-delayed negative feedback that is temperature compensated. Our results provide strong constraints for future models and emphasize the importance of studying transitory regimes along temperature effects in circadian systems.