Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

Abstract

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this “presumably transient” dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

Nonlinear phenomena in models of the circadian clock

“…We found that the oscillation period strongly depended on the degradation rates of REVERB, E4BP4 and DBP (figure 10). Since the period of the ODE models was approximately 20 h [57], we tuned the degradation rate of REVERB (γ REV ) to set the period to approximately 24 h. Simulations of the three DDE model with the published parameter set yielded 24 h oscillations [31]. The time series solutions of the eight ODE and three DDE models are shown in figure 3.…”

“…To investigate whether nonlinear phenomena appear in the mammalian molecular clock, we analysed two recent models of the mammalian circadian clockwork published by Almeida et al [57] and Schmal et al [31]. The model equations are shown in figures 7 and 8.…”

“…Thus, in the absence of accurate long-term and stationary recordings, it is challenging to apply established attractor theory and analysis [16][17][18][19][20]. Most circadian clock models have focused on the mechanisms of rhythm generation [21][22][23][24][25], on synchronization [26,27] and on entrainment to Zeitgeber signals [28][29][30][31][32]. Only a few modelling studies have been devoted to characterize experimentally observed tori, period-doubling and chaos, yet still in the presence of external forcing [28,[32][33][34][35].…”

“…Per oscillations remain with a 24 h rhythmicity (data not shown). Results are obtained by numerical integration of the equations as published by Schmal et al[31]. White vertical line indicates the default parameter value.…”

Clocks in the Wild: Entrainment to Natural Light

“…While parameter dependencies of oscillator properties such as the amplitude or free-running period are usually intertwined in complex molecular models, the Poincaré oscillator (1, 2) conveniently treats these features as independent parameters. Thus, the impact of internal clock parameters on entrainment and synchronization properties can be studied in a straightforward manner as demonstrated in several studies (Abraham et al, 2010;Granada et al, 2013;Gu et al, 2014;Tokuda et al, 2015;Myung et al, 2018;Schmal et al, 2019). In the following we will represent the circadian clock of an organism by a Poincaré oscillator (1, 2) and study its entrainment under natural light environments, using a simple celestial mechanics derivation.…”