Determine whether time-delayed negative feedback is the dominant in vivo feedback architecture

Determine whether a time-delayed negative feedback loop constitutes the dominant feedback mechanism that links the in vitro KaiABC protein oscillator to the in vivo circadian oscillator in Synechococcus elongatus PCC 7942 under low-temperature conditions, as opposed to an instantaneous temperature-dependent positive feedback, thereby establishing the relevance of the delayed negative feedback hypothesis for the in vivo clock.

Background

The study shows that both the in vitro KaiABC oscillator and the in vivo circadian oscillator in Synechococcus elongatus undergo a supercritical Hopf bifurcation upon cooling. Using Stuart–Landau (SL) analysis of the transient response, the authors demonstrate that two simple feedback scenarios can map the temperature dependence of the in vitro oscillator’s parameters onto the in vivo oscillator: (i) instantaneous, temperature-dependent positive feedback; or (ii) time-delayed negative feedback with temperature-independent coupling strength and delay.

Although their analysis favors the delayed negative feedback scenario—yielding a single, temperature-invariant set of parameters (K, τ) that explains the data—the authors explicitly acknowledge uncertainty about whether this architecture is truly the dominant feedback mechanism in vivo, noting challenges in directly relating SL parameters to measurable biochemical quantities.

References

In this context, although we favor the time-delayed negative feedback model we cannot be certain of its relevence. This uncertainty is partly because the SL in vitro description may not have a direct equivalent to simple measured quantities.

— When lowering temperature, the in vivo circadian clock in cyanobacteria follows and surpasses the in vitro protein clock trough the Hopf bifurcation  (2409.05537 - Mihalcescu et al., 2024) in Section 5 (Discussion)